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Report Issued: January 23, 2013 Disclaimer: This report is released to inform interested parties of research and to encourage discussion. The views expressed are those of the authors and not necessarily those of the U.S. Census Bureau.
RESEARCH REPORT SERIES (Statistics #2013-02)
A Comparison of Statistical Disclosure Control Methods: Multiple Imputation Versus
Noise Multiplication
Martin Klein Thomas Mathew
Bimal Sinha
Center for Statistical Research & Methodology Research and Methodology Directorate
U.S. Census Bureau Washington, D.C. 20233
A Comparison of Statistical Disclosure Control Methods:Multiple Imputation Versus Noise Multiplication
Martin KLEIN, Thomas MATHEW and Bimal SINHA
When statistical agencies release microdata to the public, a major concern is the control
of disclosure risk, while ensuring utility in the released data. Often some statistical disclosure
control methods such as data swapping, multiple imputation, top coding, and perturbation
with random noise, are applied before releasing the data. This article provides a compre-
hensive comparison of two methods, namely, multiple imputation and noise multiplication,
for drawing inference about some useful parameters under the exponential, normal and log-
normal models. The comparison is provided under two scenarios: (1) the entire data set is
replaced by multiply imputed or noise multiplied data, and (2) only the top part of the data
is similarly replaced. The latter scenario arises, for example, when top coding is used for
disclosure control, especially with income data. Methodology is developed for the analysis of
noise multiplied data under both scenarios. Under the situation where only the large values
in the dataset are noise multiplied, data analysis methods are developed and compared under
two types of data releases: (i) each released value includes an indicator of whether or not
it has been noise perturbed, and (ii) no such indicator is provided. The comparison study
shows that data analyses under the multiple imputation and noise multiplication methods
can provide similar results in terms of accuracy of statistical inferences; and that noise multi-
Martin Klein (E-mail: [email protected]) and Thomas Mathew (E-mail:[email protected]) are Research Mathematical Statisticians in the Center for Statistical Researchand Methodology, U.S. Census Bureau, Washington, DC 20233. Bimal Sinha (E-mail: [email protected]) isResearch Mathematical Statistician in the Center for Disclosure Avoidance Research, U.S. Census Bureau,Washington, DC 20233. Mathew and Sinha are also Professors in the Department of Mathematics andStatistics, University of Maryland Baltimore County, Baltimore, MD 21250. The authors are grateful toJerry Reiter for providing the data used in Section 7. They are thankful to Joseph Schafer, Eric Slud,Yves Thibaudeau, Tommy Wright and Laura Zayatz for encouragement, and to Paul Massell for somehelpful comments. This article is released to inform interested parties of ongoing research and to encouragediscussion of work in progress. The views expressed are those of the authors and not necessarily those ofthe U.S. Census Bureau.
1
plication can provide either more or less accuracy than multiple imputation by appropriately
adjusting the variance of the noise generating distribution. Extensive simulation results pro-
vide guidance as to how the noise variance affects accuracy of inference in several parametric
settings. A comparison using data from the 2000 U.S. Current Population Survey highlights
the similarities of the methods. Detailed tables summarizing simulation results and some
technical derivations are available online as supplementary material.
KEY WORDS: Customized noise distribution; EM algorithm; Partially synthetic data; Syn-
thetic data; Tuning parameter.
1. INTRODUCTION
When survey organizations and statistical agencies such as the U.S. Census Bureau re-
lease microdata to the public, a major concern is the control of disclosure risk, while si-
multaneously ensuring quality and utility of the released data. Very often some popular
statistical disclosure control methods such as data swapping, multiple imputation (MI), top
coding/bottom coding (especially for income data), and multiplication with random noise,
are applied before releasing the data. Multiple imputation has been in existence for some
time as a viable methodology to handle missing data (see Rubin, 1987); following the initial
proposal by Rubin (1993), in a series of papers (e.g., Drechsler and Reiter, 2010; Raghu-
nathan, Reiter, and Rubin, 2003; Reiter, 2003, 2004, 2005a, 2005b) Reiter and his colleagues
expanded its scope and provided a solid and rigorous foundation for its use so much so that
statistical agencies can now employ this method for sensitive data protection while data
users can carry out the required inference in a valid way. When MI is applied for statis-
tical disclosure control, the multiply imputed data that are ultimately released are usually
referred to as synthetic data. More recently, multiple imputation has been cleverly used by
2
An and Little (2007) as an alternative to top coding. Recall that top coding consists of
censoring the top part of the data above a specified threshold, and is commonly used in the
context of income data so that the identity of those in the top income bracket is protected.
We refer to the recent monograph by Drechsler (2011) for a detailed discussion of multiple
imputation as a tool for disclosure control. Noise perturbation by addition or multiplication
has also been advocated by some statisticians as a possible data confidentiality protection
mechanism (Hwang, 1986; Little, 1993; Kim and Winkler, 2003); recently there has a been
a renewed interest on this topic (Nayak, Sinha and Zayatz, 2011; Sinha, Nayak and Zayatz,
2011).
In this paper we provide a comprehensive comparison of the above two methods, namely,
multiple imputation (MI) and noise multiplication, for drawing inference about some use-
ful parameters under three parametric models. Both of these methods have been applied
to Census Bureau data products. For instance, multiply imputed synthetic data prod-
ucts have been developed and are available for the following: OnTheMap database of
commuting patterns (Machanavajjhala et al., 2008), the Longitudinal Business Database
(Kinney et al., 2011), the Survey of Income and Program Participation (Abowd et al.,
2006), and American Community Survey group quarters data (Rodriguez, 2007; Hawala,
2008). Regarding application of noise multiplied data, the first public use microdata sample
(PUMS) produced from the Survey of Business Owners (SBO) was released in August 2012
(http://www.census.gov/econ/sbo/), and noise multiplication was employed for confiden-
tiality protection of some variables. Here each record corresponds to a business surveyed in
the 2007 SBO, and a number of variables are provided relating to firm size, business char-
acteristics, and business owner characteristics. In this data product, a number of steps are
taken to protect confidentiality of businesses, and the variables relating to receipts, payroll,
and employment are rounded and multiplied by random noise prior to release (2007 Survey
of Business Owners (SBO) Public Use Microdata Sample (PUMS) Data Users Guide, 2012).
3
Given that both multiple imputation and noise multiplication are actually being employed
for disclosure limitation, a comparison between these two is clearly of practical interest. It
should however be noted that while methodology for data analysis is now well developed
in the context of multiple imputation, such is not the case for noise multiplication. Thus a
major goal of this work is the development of rigorous data analysis methodology for noise
multiplied data. We have considered three popular univariate parametric models: exponen-
tial, normal, and lognormal, and have dealt with the problem of estimation of some standard
parametric functions such as mean, variance and percentiles. We show that data analyses
under the multiple imputation method as well as under the noise multiplication method can
provide similar results in terms of accuracy of inferences, and under noise multiplication the
inferences can be made either more or less accurate through adjustment of the variance of
the noise generating distribution; in this sense, noise multiplication does offer some flexibility
compared to multiple imputation.
When multiple imputation (MI) and noise multiplication (NM) are applied to the entire
data at hand, we will refer to the scenario as total MI and fully NM case. Often times there
are situations when a part of the data is sensitive and must not be released while the rest
of the data can be used/released without any compromise. This is the set up of top coding
mentioned above, where values above a certain threshold C are suppressed and only the
number of values in the data set above C are reported along with the actual values below C.
This is precisely the scenario considered by An and Little (2007), and they have developed
data analysis methods based on multiple imputation of the data above C, in combination
with the original values below C. We can also consider noise multiplication of the values
above C, and release the data consisting of such noise multiplied values, along with the
actual observations below C. Again, we will provide a comparison of An and Little’s (2007)
multiple imputation along with the noise multiplication idea just mentioned, for the three
parametric models mentioned earlier. Under the scenario of noise multiplication of only
4
values above the threshold C, we consider two types of data releases referred to as cases (i)
and (ii). In case (i) data release, each released variable includes an indicator of whether or
not it has been perturbed, while in case (ii), no such indicator is provided. Data analysis
methods for both of these cases are developed in Section 3. Naturally, case (i) data appear to
carry more information than case (ii) data, and so one would expect that case (i) would lead
to more accurate inference than case (ii), perhaps at an increased disclosure risk. The case
(i) data always yield more (or equally) accurate inferences than a top coded sample, whereas
depending on the magnitude of the noise variance, case (ii) data can yield either more or less
accurate inference than a top coded sample; we elaborate and justify these points in Section
6.
Here is the organization of the paper. In Section 2 we provide details of the statistical
analysis for the case of fully noise perturbed data. Section 3 deals with developing statistical
analysis based on noise perturbation of only top-coded data, keeping the rest of the data
(below C) as it is. Appendix A provides proof of a technical result used in Section 3 and
states some related results. Following the work of Reiter (2003) and An and Little (2007),
we provide a brief review of the multiple imputation method for both the total MI and top-
coded data situations in Section 4. Section 5 briefly mentions statistical data analysis under
usual top coding so that we have censored data. Conclusions based on extensive numerical
results are given in Section 6. In Section 7, an application using data from the 2000 U.S.
Current Population Survey is given to illustrate the similarities of the methods. The data
comprise of seventeen (17) variables measured on 51,016 heads of households (see Table 1 in
Drechsler and Reiter, 2010, for a description of ten variables) including age, race, sex and
marital status as key identifiers, and a mix of other categorical and numerical variables with
non-Gaussian distributions, and with large percentages of values equal to zero. We have
selected two such numerical variables with extreme sample sizes, namely, total household
income with sample size = 50,661 and household alimony payment with sample size 206, and
5
have carried out the analysis (after deleting the zero values). It turns out that a lognormal
distribution fits both the datasets well, and the inferences drawn upon the original mean
and variance and the log-scale mean and variance are comparable under the two methods:
multiple imputation and noise multiplication with noise variance not exceeding 10%. In fact,
the inferences closely reproduce those based on the original data. We conclude the paper
with a summary and recommendations in Section 8.
We end this section with two general observations. First, while standard and often op-
timum parametric inference can be drawn for the three chosen simple probability models,
such an analysis is far from being close to optimum or even simple when noise multiplication
(NM) is used, either with full data or with top-coded data. We have essentially relied on
the asymptotic theory, providing enough computational details of the MLEs and observed
Fisher information matrices in each case. Second, we should point out that our approach to
modify the microdata to protect the confidentiality of all records and carry out the analysis
based on noise-modified microdata data is different from modifying the microdata when the
goal is to release tables (Evans, Slanta, and Zayatz, 1998). Moreover, the focus of this paper
is on data analysis methods based on noise-modified microdata rather than on a study of
the effectiveness of the procedures in protecting the data.
2. DATA ANALYSIS UNDER FULL NOISE MULTIPLICATION
The problem of statistical data analysis under full noise perturbation, although old (see
Hwang, 1986; Little, 1993; Kim and Winkler, 2003), has been recently revisited, and some
new and interesting results have emerged in a nonparametric setup for estimation of the
moments and for inference about the quantiles of a variable Y based on noise multiplied
data (Nayak, Sinha and Zayatz, 2011; Sinha, Nayak and Zayatz, 2011). Briefly, Nayak et
al. (2011) discussed at length various issues related to the statistical properties of random
6
noise perturbation methods for data masking. Under the noise multiplication scenario, issues
such as confidentiality protection, moment estimation, properties of balanced noise distribu-
tion, and effects on data quality and privacy protection in the context of tabular data were
addressed at length. In a subsequent paper, Sinha et al. (2011) proposed some inferential
procedures for quantile estimation based on noise multiplied micro data. It turns out that
this is indeed a difficult inferential problem, and an empirical Bayes solution based on a
nonparametric model was developed by the authors.
As far as we know, efficient model-based parametric inference procedures based on noise
perturbed data are still lacking, with the sole exception of the work by Little (1993) where
inference under noise multiplication is briefly mentioned, with a remark that ...this approach
does not yield valid inferences for parameters..... Denoting by y1, . . . , yn a random sample of
size n from the distribution of Y ∼ fθ(y), with unknown parameter θ, and by R ∼ h(r) the
underlying noise variable (with a completely known distribution h(r)), the noise perturbed
data z = (z1, . . . , zn) with zi = yi×ri can be thought of as a random sample from Z ∼ gθ(z) =∫fθ(
zr)h(r)dr
r. The noise variables r1, . . . , rn are independent and identically distributed
(iid) as R, and it is assumed that R is a nonnegative random variable. We assume that
both Y and R are continuous random variables. When the parameters θ have moment-type
interpretations based on Y , they admit simple unbiased (not necessarily optimum) estimates
based on z (see Hwang, 1986; Nayak et al., 2011); however, efficient inference for θ based on
z is far from being simple due mainly to the possible complexity of gθ(z). In the context of
masking by noise multiplication, unlike our setup where R has a specified noise distribution,
independent of the data Y , Kim (1986), Sullivan and Fuller (1989, 1990) and Little (1993)
dealt with the case when R is made data-dependent! This procedure, while it keeps intact
certain basic moments of the original data, obviously renders considerable difficulty in the
inference process. In this context, it is rather interesting to quote Little (1993), which
indeed provides a compelling motivation for our research: Although a full likelihood-based
7
analysis may not be feasible in many settings, I think the modeling perspective provides a
useful basis for assessing simpler approximate methods. Future work might provide more
detailed applications of the modeling approach to specific masking procedures. Our goal here
is to provide exact and approximate efficient inference procedures when noise multiplication
is used as a data masking mechanism.
Here is a brief outline of our approach. In view of the anticipated complexity of the
marginal likelihood based on z, we can apply the familiar EM algorithm to compute the MLE
of θ (Little and Rubin, 2002). It is also possible to use a parametric bootstrap procedure
to study the frequentist properties of the MLE (Efron and Tibshirani, 1994). However we
instead derive the observed Fisher information matrices and use them to estimate standard
deviation in our extensive simulations. We construct 95% confidence intervals as (MLE)
± (1.96 × estimated standard deviation). Under the EM framework, we can write uobs =
(z1, ...., zn), umis = (r1, ...., rn), uc = (uobs,umis), to denote the observed data, missing data
and complete data, respectively. Using the notations in the previous paragraph, the complete
data likelihood can obviously be expressed as L(θ|uc) =∏n
i=1[fθ(ziri
)h(ri)ri
] and the observed
data likelihood as L(θ|uobs) =∏n
i=1[∫fθ(
ziri
)h(ri)ridri].
Taking logarithm, if `(θ|uc) = lnL(θ|uc) (ignoring constants), the E-step is then carried
out by starting with the estimate θ(t) (at the tth step) and computing
Q(θ|θ(t)) = Eθ(t) [`(θ|uc)|uobs] = Eθ(t)
[n∑i=1
ln fθ(ziri
)|z1, ...., zn
]=
n∑i=1
Eθ(t)
[ln fθ(
ziri
)|zi]
(1)
and the M -step is carried out by maximizing Q(θ|θ(t)) with respect to θ, resulting in θ(t+1). It
would be rather easy to evaluate the one dimensional integral (with respect to r) in Q(θ|θ(t))
above, either explicitly or numerically. The iteration defined through the E and M -steps
can then be run until a stopping criterion is met. For many choices of fθ(y), the M-step will
have a closed form expression. The E-step is also quite feasible since the one-dimensional
8
integrals appearing in (1) are straightforward to evaluate using numerical or Monte Carlo
methods.
As for the noise distribution, we have taken a popular choice R ∼ h(r) ∼ Uniform(1 −
ε, 1 + ε) for some 0 < ε < 1 with E(R) = 1 and var(R) = σ2r = ε2/3. Computation of the
MLEs, and the derivation of the observed Fisher information are both described in Appendix
B of the supplementary material for the exponential, normal and lognormal models. For
exponential and lognormal distributions, we have also used what we call customized noise
distributions that can provide simplified inference because they permit closed form evaluation
of gθ(z). These are given by
Under the exponential distribution : R ∼ hδ(r) =δδ+1
Γ(δ + 1)r−δ−2e−
δr , δ > 1,
Under the lognormal distribution : R ∼ lognormal with lnR ∼ N(−ψ2
2, ψ2).
3. DATA ANALYSIS UNDER NOISE MULTIPLICATION OF EXTREME VALUES
We now consider the set up where top coding is used for disclosure control. The random
variables yi, ri, and zi, i = 1, ...., n, are as defined in Section 2. Now, any observation yi
which exceeds a specified threshold C > 0 is considered sensitive and, under top coding such
values are simply not reported. Another option is to report zi, the noise perturbed version
of yi, along with an indicator that the true value has been perturbed. More precisely, for
i = 1, ...., n, let us define
∆i = I(yi ≤ C), and xi =
yi, if yi ≤ C,
zi, if yi > C.(2)
Inference for θ will be based on {(x1,∆1), ...., (xn,∆n)}, or based on {x1, ...., xn}. We note
that the latter data do not directly identify which observations have been perturbed, and
9
hence provide more disclosure control than the former. The expression for the joint distri-
bution of (xi, ri,∆i), which is crucial for our purpose, is given by the following proposition,
whose proof appears in Appendix A.
Proposition 1. The joint pdf of (xi, ri,∆i) is given by
kθ(xi, ri, δi) =
fθ(xi)h(ri), if xi < C, 0 < ri <∞, δi = 1,
fθ(xi/ri)h(ri)(1/ri), if 0 < ri < xi/C, δi = 0,
0, if δi = 0, ri > xi/C,
or if δi = 1, xi > C.
(3)
Proposition 1 can be used to derive the likelihood function of θ based on data of the two
types: {(x1,∆1), ...., (xn,∆n)} and (x1, ...., xn); details appear in Appendix A. We refer to
the former data type as case (i), and the latter as case (ii). Letting kθ(x, δ) and kθ(x) be the
densities defined in Appendix A, we now describe details of the computation of the maximum
likelihood estimate of θ based on the EM algorithm. We shall separately consider cases (i)
and (ii).
Case (i): Observed data consist of {(x1,∆1), ...., (xn,∆n)}.
In order to describe the EM algorithm under this setting, we define the observed, miss-
ing, and complete data, respectively, as follows: vi,obs = (x1, ...., xn,∆1, ....,∆n), vi,mis =
(r1, ...., rn), vc = (vi,obs,vi,mis). By Proposition 1, the joint density function of vc is∏ni=1[fθ(xi)h(ri)]
∆i [fθ(xi/ri)h(ri)(1/ri)]1−∆i , and thus we define the complete data likelihood
function as L(θ|vc) =∏n
i=1 fθ(xi)∆ifθ(xi/ri)
1−∆i , and the complete data log-likelihood func-
tion as
`(θ|vc) =n∑i=1
{∆i ln f(xi; θ) + (1−∆i) ln fθ(xi/ri)} . (4)
10
The E and M -steps are then computed as follows.
E-step. To carry out the E-step, we compute:
Q(θ|θ(t)) = Eθ(t) [`(θ|vc)|vi,obs]
=n∑i=1
{∆i ln fθ(xi) + Eθ(t) [(1−∆i) ln fθ(xi/ri)|xi,∆i]}
=n∑i=1
{∆i ln fθ(xi) + (1−∆i)Eθ(t) [ln fθ(xi/ri)|xi,∆i = 0]}
=n∑i=1
{∆i ln fθ(xi) + (1−∆i)ψ(xi, θ
(t), θ)}, (5)
where
ψ(xi, θ(t), θ) ≡ Eθ(t) [ln fθ(xi/ri)|xi,∆i = 0]
=
∫ ∞0
[ln fθ(xi/ri)]kθ(t)(xi, ri,∆i = 0)
kθ(t)(xi,∆i = 0)dri
=
∫ xi/C0
[ln fθ(xi/ri)]fθ(t)(xi/ri)h(ri)r−1i dri∫ xi/C
0fθ(t)(xi/ω)h(ω)ω−1dω
. (6)
M-step. If θ(t) is the current estimate of θ, then the M step updates the current estimate to
θ(t+1) = arg maxθQ(θ|θ(t)).
Case (ii): Observed data consist of only (x1, ...., xn).
To describe the EM algorithm in this setting, we re-define the observed and missing
data, respectively, as vii,obs = (x1, ...., xn), vii,mis = (r1, ...., rn,∆1, ....,∆n). The complete
data vc = (vii,obs,vii,mis) remains the same as in case (i), and hence the complete data
log-likelihood function is given by (4). The E and M -steps are then modified as follows.
11
E-step. To carry out the E-step, we now compute:
Q(θ|θ(t)) = Eθ(t) [`(θ|vc)|vii,obs]
=n∑i=1
{Eθ(t) [∆i|xi] ln fθ(xi) + Eθ(t) [(1−∆i) ln fθ(xi/ri)|xi]}
=n∑i=1
{ψ1(xi, θ
(t)) ln fθ(xi) + ψ2(xi, θ(t), θ)
}, (7)
where
ψ1(xi, θ(t)) = Eθ(t) [∆i|xi] = Prθ(t) [∆i = 1|xi] =
kθ(t)(xi,∆i = 1)
kθ(t)(xi)
=I(xi < C)fθ(t)(xi)
I(xi < C)fθ(t)(xi) + I(xi > 0)∫ xi/C
0fθ(t)(xi/ω)h(ω)ω−1dω
, (8)
and
ψ2(xi, θ(t), θ) = Eθ(t) [(1−∆i) ln fθ(xi/ri)|xi]
=1∑
∆i=0
∫ ∞0
(1−∆i)[ln fθ(xi/ri)]kθ(t)(xi, ri, δi)
kθ(t)(xi)dri
=
∫ ∞0
[ln fθ(xi/ri)]kθ(t)(xi, ri, δi = 0)
kθ(t)(xi)dri
=
∫ xi/C0
[ln fθ(xi/ri)]fθ(t)(xi/ri)h(ri)r−1i dri
I(xi < C)fθ(t)(xi) + I(xi > 0)∫ xi/C
0fθ(t)(xi/ω)h(ω)ω−1dω
. (9)
M-step. As usual, if θ(t) is the current estimate of θ, then the M step updates the current
estimate to θ(t+1) = arg maxθQ(θ|θ(t)).
Application of the above computational steps to the exponential, normal and lognormal
models is explained in Appendix C of the supplementary material, and expression for the
observed Fisher information are provided.
12
4. DESCRIPTION OF MULTIPLE IMPUTATION METHODS
In the context of statistical disclosure control, MI is used to create public use data that
protect confidential records from disclosure, while still yielding valid inferences for population
quantities. The MI methodology is generally motivated from a Bayesian perspective, but it
has been shown that the inferences obtained are often properly calibrated in the frequentist
sense; we refer to the references given above. To implement this method, the data collector,
who would have access to the confidential records, formulates an appropriate model for the
data. To complete the Bayesian model specification, noninformative prior distributions are
usually placed on model parameters. A public use data file is then created by deleting all
confidential records (which may include all or part of the data) and imputing the deleted
values, say m > 1 times, using m independent draws from the posterior predictive distribu-
tion. Hence, the public use file appears as m data sets, each of the same structure as the
original, but with confidential records replaced by imputed values. Such a public use file is
referred to in the literature as a synthetic data file. The number of imputations m is chosen
to be larger than 1, often in the range of 5-10, which allows the additional variance due
to imputation to be properly incorporated into the inferences obtained from the synthetic
data. The above is a brief general description of MI for statistical disclosure control which
is based on the method of Reiter (2003). Variants of this method have also appeared in the
literature, appropriate for certain types of data; these include imputing the population m
times, and then sampling from each synthetic population as in Raghunathan, Reiter, and
Rubin (2003).
We now briefly review the MI methods which are applicable to the two general scenarios
considered in this paper: (1) the case of total MI, which serves as a competitor to the noise
perturbation methods developed in Section 2, and (2) the case of MI for extreme values only,
which serves as a competitor to the noise perturbation methods developed in Section 3. The
13
original data are assumed to consist of an iid sample y = (y1, ...., yn) from a parametric model
fθ(y), and we place a noninformative prior distribution p(θ) on the unknown parameter θ.
We let Q = Q(θ) denote the population quantity that we wish to draw inference upon, using
the multiply imputed data. For ease of presentation, we assume Q is a scalar. Inferences
for Q are obtained from the synthetic data as follows. Let q = q(y) denote an estimator
of Q that is computed from the original data, and let v = v(y) denote an estimator of the
variance of q, also computed from the original data. For instance, q may be the maximum
likelihood estimator of Q, and v may be the estimated asymptotic variance obtained from
the inverse of the observed Fisher information matrix. Let y∗(1), ....,y∗(m) denote the m sets
of multiply imputed/synthetic data. We discuss how to generate these multiply imputed
data sets in the subsections below. Given the synthetic data, one then proceeds to compute
qj = q(y∗(j)) and vj = v(y∗(j)), the analogs of q and v, on the jth synthetic data set, for
j = 1, ....,m. The appropriate MI estimators for the settings considered here are given by
Reiter (2003). The MI estimator of Q is qm = 1m
∑mj=1 qj, and the estimator of the variance
of qm is Tm = bm/m + vm, where bm = 1m−1
∑mj=1(qj − qm)2 and vm = 1
m
∑mj=1 vj. We next
discuss the generation of y∗(1), ....,y∗(m) for the cases of total MI, and MI for extreme values.
4.1 Total MI
In the case of total MI, the entire original data set is confidential. Thus, as a method
of statistical disclosure control, total MI serves as an alternative to the noise multiplication
methods developed in Section 2. The posterior distribution is obtained as usual via Bayes
theorem: p(θ|y) ∝ p(θ)×∏n
i=1 fθ(yi). The synthetic data are then obtained as follows.
1. Draw θ∗ from the posterior distribution p(θ|y).
2. Draw y∗ = (y∗1, ...., y∗n) as iid from fθ∗(y).
Steps (1) and (2) above are repeated independently m times to obtain y∗(1), ....,y∗(m), the
14
multiply imputed/synthetic data. The notation fθ∗(y) denotes the pdf fθ(y) with the un-
known parameter θ set equal to θ∗.
4.2 MI for Extreme Values
In the case of MI for extreme values, only those data values above a known threshold
C are considered to be confidential. Thus, as a method of statistical disclosure control, MI
for extreme values serves as an alternative to the noise multiplication methods developed in
Section 3. In this scenario, we consider two MI methods presented by An and Little (2007),
namely, parametric MI based on complete data (PMIC) and parametric MI based on deleted
data (PMID). We now briefly describe these methods. Although it is only the values above
C that are considered sensitive, a cut-point CI < C is selected, and any value yi > CI is
imputed. As discussed by An and Little (2007), by choosing the cut-point CI to be less than
C, a mixing of sensitive and non-sensitive values is achieved, which should enhance the level
of protection against disclosure. Let y = (yret,ydel) where yret = {yi : yi ≤ CI} denotes the
values in y that will be retained, and ydel = {yi : yi > CI} denotes the values in y that will
be deleted.
The PMIC method proceeds as follows. One first fits the parametric model to the com-
plete data y, and thus obtains the posterior distribution p(θ|y) ∝ p(θ)×∏n
i=1 fθ(yi). Then
the synthetic data are generated as follows.
1. Draw θ∗ from the posterior distribution p(θ|y).
2. Obtain the imputed data y∗del, which is of the same length as ydel, by taking iid draws
from the truncated version of fθ(y) defined as f(CI ,∞)(y|θ∗) =fθ∗ (y)×I(CI,∞)(y)∫∞
CIfθ∗ (u)du
.
Steps (1) and (2) above are repeated independentlym times to obtain y∗(1)del , ....,y
∗(m)del . Finally,
we obtain the synthetic data as y∗(j) = (yret,y∗(j)del ), j = 1, ....,m.
Now we describe the PMID method. In the PMID method, one fits the parametric model
to the deleted data ydel instead of the complete data. That is, the posterior distribution of θ
15
is computed as p(θ|ydel) ∝ p(θ)×∏{i:yi∈ydel} fθ(yi), and synthetic data are generated through
the following steps.
1. Draw θ∗ from the posterior distribution p(θ|ydel).
2. Obtain the imputed data y∗del, which again is of the same length as ydel, by taking iid
draws from fθ∗(y). Note here that we do not draw from the truncated distribution as
in PMIC.
As usual, steps (1) and (2) above are repeated independently m times to get y∗(1)del , ....,y
∗(m)del ,
and the synthetic data are then obtained as y∗(j) = (yret,y∗(j)del ), j = 1, ....,m. A comparison
of PMID and PMIC methods will be reported later, based on numerical results.
4.3 Details for the Exponential, Normal and Lognormal Distributions
We now briefly review the forms of the prior and posterior distributions under the ex-
ponential, normal, and lognormal models. In the following, we present the form of the
posterior assuming that the complete data y are used to fit the model. We also use the
notation y to denote the observed data. The necessary adjustments for the PMID method
are straightforward.
Exponential distribution. In this case we have fθ(y) = 1θe−y/θ, 0 < y < ∞, and we take
the improper uniform prior p(θ) ∝ 1, 0 < θ < ∞. The posterior distribution is readily
obtained as
p(θ|y) =(∑n
i=1 yi)n−1
Γ(n− 1)θ−(n−1)−1e−(
∑ni=1 yi)/θ, 0 < θ <∞,
which has the form of an inverse gamma distribution. That is, (θ−1|y) ∼ Gamma(n− 1, 1∑n
i=1 yi
).
Normal distribution. In this case we have fθ(y) = 1σ√
2πe−(y−µ)2/(2σ2), −∞ < y <∞, θ =
(µ, σ2), and we specify a standard noninformative prior which places a uniform distribution
on (µ, lnσ) and assumes these two quantities to be independent a priori. Equivalently, the
16
prior on (µ, σ2) is p(µ, σ2) ∝ (σ2)−1,−∞ < µ <∞, 0 < σ2 <∞. The posterior distribution
is then readily obtained as p(µ, σ2|y) = p(µ|σ2,y)p(σ2|y) where
(σ2|y) ∼ (n− 1)s2
χ2n−1
, (µ|σ2,y) ∼ N(y, σ2/n),
with y = 1n
∑ni=1 yi and s2 = 1
n−1
∑ni=1(yi − y)2 (Gelman et al., 2003).
Lognormal distribution. In this case we have fθ(y) = 1yσ√
2πe−(ln y−µ)2/(2σ2), 0 < y < ∞,
θ = (µ, σ2). But since ln yi ∼ N(µ, σ2), we simply apply the normal distribution results
upon replacing yi by ln yi, CI by lnCI , and C by lnC.
5. ANALYSIS OF TOP CODED DATA
The statistical analysis of top coded data is essentially asymptotic in nature, based on the
MLEs of the parameters and the observed Fisher information. The MLE computation along
with the expressions for the observed Fisher information matrix for the three parametric
models are explained in Appendix D of the supplementary material.
6. NUMERICAL RESULTS
In order to compare multiple imputation with noise multiplication in terms of accuracy
of the inference, we performed a rather extensive simulation study in the context of the one
parameter exponential distribution, the normal distribution, and the lognormal distribution.
Furthermore, under each distribution, we considered the case of full noise perturbation and
total multiple imputation, as well as the case of noise perturbation and multiple imputation
for the situation of top coded data. Tables resulting from the simulation study are provided
in Appendix E of the supplementary material.
17
The setups considered for the simulation are as follows. For the exponential distribution,
the mean was chosen to be one, and the inference problem considered is the point and
interval estimation of the mean. For the normal and lognormal distributions, simulations
were done under the parameter choices µ = 0 and σ2 = 1. For the normal distribution,
point and interval estimation were considered for the mean, variance, 84th percentile (i.e.,
µ+σ) and the 95th percentile (i.e., µ+1.645σ). For the lognormal distribution, inferences on
the same parameters, namely, µ, σ2, the 84th percentile (i.e., eµ+σ) and the 95th percentile
(i.e., eµ+1.645σ) were considered as well as those for the lognormal mean (eµ+σ2
2 ) and the
lognormal variance (e2µ+2σ2 − e2µ+σ2). A nominal confidence level of 95% was used in all
interval estimation problems. For the point estimates of the various parameters, the following
quantities were estimated by Monte Carlo simulation based on 5000 iterations: the root
mean squared error (RMSE), bias, standard deviation (SD), and expected value of estimated
standard deviation (SD). For the confidence interval, the coverage probability was estimated
and the expected length of the nominal 95% two-sided confidence interval was calculated
relative to that based on the complete data (unmasked). To facilitate the comparison, all
results shown for unmasked data are based on MLEs, observed Fisher information, and
confidence intervals of the form (MLE) ± (1.96 × estimated standard deviation). For top-
coding two choices were made for the threshold C: the 90th and 95th percentiles of each
distribution.
We shall now explain the notations used in the tables regarding the multiple imputation
and noise multiplication scenarios used in the simulations. The notation CD denotes the case
of complete data without any masking. MI denotes multiple imputation used to generate
fully masked data. MI.C and MI.D are used to denote parametric multiple imputation based
on the complete data, and based on the deleted data, respectively. These are explained in
Section 4.2. In the case of a top coded sample with a top coding threshold C, values beyond
a threshold CI were also replaced with imputed values, where CI < C, following An and
18
Little (2007). Two choices were made for CI following the recipe prescribed by An and
Little (2007). If nS denotes the number of values beyond the top coding threshold C, the
two choices of CI correspond to thresholds for which 2nS values in the sample are larger,
and 4nS values are larger. Since these values approximately correspond to the 90th and 80th
percentiles of the distribution when C is the 95th percentile, these are denoted (following
An and Little, 2007) by MI.C90 and MI.C80, respectively, in the case of multiple imputation
based on the complete data, and denoted by MI.D90 and MI.D80, respectively, in the case of
multiple imputation based on the deleted data. Throughout we have used 50 sets of imputed
values under MI.
The notations used under noise multiplication are as follows. We have used either a
Uniform(1− ε, 1+ ε) distribution or a customized distribution for generating the noise multi-
pliers. In the case of Uniform(1− ε, 1 + ε), the notation NM10U denotes noise multiplication
with the above uniform distribution under the choice ε = 0.10. NM20U, NM30U etc. are
similarly defined. Furthermore, NM10C, NM20C etc. are the corresponding notations under
the customized prior whose mean and variance match those of the respective uniform distri-
butions. Additional notation used under the uniform noise distribution Uniform(1− ε, 1 + ε)
is as follows. For the choice ε = 0.1, NM10.1 and NM10.2, respectively, represent the case of
observing the (xi,∆i)s, or only the xis; these are Case (i) and Case (ii) explained in Section 3
for the three different distributions. NM20.1, NM20.2 etc. are similarly defined. In addition
to the above notations, entries in the tables corresponding to CENS denote results from the
analysis of the censored data, i.e., the top coded data.
The statistical computing software R (R Development Core Team, 2011) was used for all
computations and the integrate function in R was used to evaluate the required univariate
integrals that could not be obtained in closed form. We shall now summarize the conclusions
emerging from the extensive numerical results with detailed tables appearing in Appendix
E of the supplementary material.
19
The Exponential Distribution.
For the case of fully masked data, confidence interval coverage probabilities resulting
from noise multiplication are not satisfactory for small sample sizes; see the entries in the
tables (supplementary material) corresponding to the sample size of 30. However, asymp-
totic inference based on the unmasked data also yields unsatisfactory coverage probability
when n = 30. Interestingly, even in this case where the sample is as small as n = 30,
multiple imputation does provide satisfactory coverage probability. The numerical results
corresponding to sample size of 50 or more show that the coverages are quite satisfactory
under the various noise multiplication scenarios, and under multiple imputation. As the
noise variance increases, the relative length increases, as expected. The RMSE values, SD,
and relative length each appear to show an increasing trend as the noise variance goes up,
but an increasing trend in the bias is not always present in the numerical results. In terms
of RMSE and relative length of confidence intervals, the noise multiplication yields results
similar to MI when ε is about 0.3 or 0.4. For smaller (larger) values of ε, the noise multi-
plication generally yields smaller (larger) RMSE and narrower (wider) confidence intervals.
In terms of bias, a much larger bias has been noted under multiple imputation, compared
to all scenarios of noise multiplication. We note that the uniform and customized noise dis-
tributions generally give similar results, with the customized distribution providing slightly
more accurate inference than uniform when ε is large.
In the case of multiple imputation and noise multiplication for top coded data, the
performance of MI.C80 and MI.C90 are not satisfactory, even for samples as large as 2000, as
the true confidence interval coverage is below the nominal level. However, both MI.D80 and
MI.D90 are satisfactory for various sample sizes, even for sample size as small as 100. All the
noise multiplication scenarios provide satisfactory coverage probabilities. The entries under
CENS show that the top coding method itself provides satisfactory coverage probabilities,
but it tends to be less accurate than the noise multiplication methods unless ε is quite large.
20
Interestingly, for n = 100 and n = 200, the top coded data and noise multiplied data (even
with large ε = 0.90) yield more accurate inferences than MI.D80 and MI.D90 in terms of
RMSE and confidence interval length. For n = 1000 and n = 2000 the noise multiplied data
are generally more or equally accurate than MI.D80 and MI.D90 for ε ≤ 0.5 or 0.6. In our
numerical results, the CENS method (top code data) never provide more accurate inference
(in terms of RMSE and confidence interval length) than the case (i) noise multiplied sample,
but they do sometimes provide more accurate inference than a case (ii) noise multiplied
sample when ε is large. At the end of this section, we explain this finding, which holds
for all three distributions considered. As one would expect, the case (i) noise multiplied
sample (xi,∆i), i = 1, . . . , n, provides greater accuracy of inference than the case (ii) noise
multiplied sample x1, . . . , xn. Regarding MI.D80 versus MI.D90, with the larger sample sizes
n = 1000 or 2000 the two methods are mostly similar. Interestingly, in the smaller sample
sizes n = 100 or 200, the MI.D90 method, which imputes less data than MI.D80, but also
uses less data to fit the imputation model, is less accurate than the MI.D80 method. The
remaining conclusions are similar to those noted above for the case of fully masked data; a
rather large bias has been noted under multiple imputation.
The Normal Distribution
Under full masking of the data, for estimating the normal mean, the results are compa-
rable under multiple imputation and noise multiplication when ε is equal to about 0.4 or
0.5 (depending on the sample size). By choosing ε less than or greater than 0.4 or 0.5, the
results under noise multiplication can be made more or less accurate than multiple impu-
tation, respectively. However, for estimating the variance under the smaller sample sizes of
n = 30, 50, 100, multiple imputation appears to have an edge in terms of coverage probabil-
ity and relative length, and in terms of the other quantities. For estimating the variance,
the asymptotic confidence intervals based on unmasked data and noise multiplied data all
21
have coverage probability below nominal, while confidence intervals based on multiply im-
puted data have closer to nominal coverage probability. This effect diminishes for both the
unmasked and noise multiplied data for the larger sample sizes n = 200, 1000, 2000. For
estimating the percentiles, the results are mostly similar between multiple imputation and
noise multiplication and one can locate a value of ε (e.g., ε = 0.2 or 0.3 here) at which the
inferences have nearly equivalent accuracy.
Under noise multiplication or multiple imputation for top coded data, MI.C90 and
MI.C80 again have poor coverages even with large samples. With the smaller sample size of
n = 100 we notice that when the parameter of interest is the variance σ2 or µ + σ2/2 the
MI.D90 method can yield a huge RMSE, bias, SD, and relative confidence interval length,
while the coverage probability is maintained at the nominal level. Such inaccurate inference
occurs under MI.D90 because when n = 100 and C is the 95th percentile, there is a non-
negligible probability that the number of data points used to fit the imputation model can be
as small as 2 if nS = 1 (refer to Section 4.2); and when this happens there is a non-negligible
probability that the posterior draw for σ2 is huge. Apart from this anomaly in MI.D90, the
results between MI.D90, MI.D80 and the noise multiplication methods are generally similar
with the MI.D methods often yielding a noticeably high level of accuracy in terms of RMSE,
SD, and relative confidence interval length. It is interesting that in the normal case the MI.D
methods generally yield highly accurate inference, whereas in the exponential case, we noted
that their accuracy was somewhat low, sometimes lower than top coding. In each case one
can determine an ε at which the noise multiplied data provide a similar level of accuracy
as MI. For instance when estimating the normal mean, a value of ε = 0.4 generally gives a
similar level of accuracy as the MI.D methods.
The Lognormal Distribution
For fully masked data, when estimating the log scale mean µ, the results are very much in
22
line with those noted above for the normal case for estimation of the normal mean. Similarly,
when estimating the log scale variance σ2, the results are in line with the findings noted above
for the normal case for estimation of the normal variance. With the smaller sample sizes of
n = 30, 50, 100, the noise multiplied data and unmasked data also provide less than nominal
confidence interval coverage when the parameter of interest is the lognormal mean, lognormal
variance, the 84th percentile and the 95th percentile. Multiple imputation provides closer to
nominal coverage probability in these cases. For the larger sample sizes n = 200, 1000, 2000,
this effect diminishes. Regarding the choice of uniform vs. customized noise distributions,
the findings are similar to those of the exponential case.
For noise multiplication or multiple imputation for top coded data, we note that MI.C90
and MI.C80, exhibit poor confidence interval coverages, similar to what has been noted
earlier. When the parameter of interest is the variance, lognormal mean, lognormal variance,
84th percentile, or 95th percentile, and when n = 100 or 200, the MI.D80 and MI.D90
methods can yield huge RMSE, bias, SD and relative confidence interval length. This effect
occurs for reasons similar to those noted above for the normal case, namely, there is a non-
negligible probability that the number of data points available to fit the model is as small as
four (MI.D80) or two (MI.D90), i.e., nS = 1. In these cases the noise multiplication methods
can still provide reasonable results. In larger sample sizes, the multiple imputation and noise
multiplication methods both provide reasonably accurate results, and one can select an ε at
which their accuracy is nearly equivalent (in some cases such as when estimating the log
scale mean, the ε value can be fairly large).
Remarks on Noise Multiplication Versus Top Coding at C
1. If we observe noise multiplied data under case (i) of Section 3, then a top coded
sample can be re-constructed from the observed data. However, a case (i) noise multiplied
sample cannot be constructed from the top coded data. So in this sense, case (i) noise
23
multiplied data carry more information than top coded data. The simulation results confirm
this statement because the case (i) noise multiplication method generally leads to a shorter
confidence interval and smaller SD than top coding for all values of ε that we consider. As
ε increases, the case (i) noise multiplication method begins to yield results which are quite
similar to top coding, as one would expect.
2. Suppose we observe noise multiplied data under case (ii) of Section 3 and the noise
density is Uniform(1− ε, 1 + ε). Then the top coded sample cannot be re-constructed from
these observed data because for any xi such that (1 − ε) × C < xi < C, we do not know
whether or not this xi was noise perturbed. Of course, we also cannot re-construct a case
(ii) noise multiplied sample based on only the top coded data. Therefore, depending on the
value of ε, the case (ii) noise multiplied sample may contain either more or less information
than the top coded sample. The simulation results confirm this statement since for small ε,
the case (ii) noise multiplication scenario leads to a shorter confidence interval and smaller
SD than top coding. When ε becomes large, this situation is reversed. It is interesting to
note that given the noise multiplied data under case (ii), we could construct a top coded
sample with a lower top code value of (1− ε)× C.
7. DATA ANALYSIS
In this section we provide an application based on data from the 2000 U.S. Current
Population Survey which has been thoroughly and repeatedly analyzed in Reiter (2005c,d;
2009) and Drechsler and Reiter (2010) for illustrating various aspects of multiple imputation
methodology. Here we shall use the data on two variables whose distributions can be well
approximated by the lognormal distribution. We shall report the analysis based on full noise
multiplication and total MI (Tables F1 and F2 in Appendix F of the supplementary material).
We shall also top code 10% of the data and then report the analysis based on the full data
24
sets, the censored data sets resulting from top coding, the data sets obtained by multiple
imputation of the top coded values, and the data sets resulting from noise multiplication of
the top coded values (Tables 1 and 2). This will of course permit us to compare the results
of the different analysis for the two data sets.
The entire data comprise of seventeen variables measured on 51,016 heads of households
(see Table 1 in Drechsler and Reiter, 2010 for a description of nine variables) including age,
race, sex and marital status as key identifiers, and a mix of other categorical and numerical
variables with non-Gaussian distributions (with large percentages of values equal to zero).
We have selected two such numerical variables with extreme sample sizes, namely, total
household income with sample size = 50,661 and household alimony payment with sample
size 206, deleting the 0 values, and have carried out the analysis. It turns out that a lognormal
distribution fits both the datasets well.
Results of the analysis are given in the Tables 1 − 2 (and Tables F1 − F2 of the supple-
mentary material). As in the previous section, we used the statistical computing software R
(R Development Core Team, 2011) for all computations, and 50 multiple imputations were
used in the MI methods. The notations used in the tables are as explained in Section 6. In
addition, Est denotes point estimate of the parameter and Rel. Len. denotes the length of
a 95% confidence interval, relative to that of the interval based on the complete data. We
note that as with simulated data the conclusions about the common parameters of interest
are similar based on multiple imputation and noise perturbation (with noise variance not
exceeding about 8.33%, ε = 0.5 in uniform case) and both almost reproduce the estimates
based on the original unmasked data. It is interesting to note from Table 1 (total household
income) that the MI.C methods yield considerably wider confidence intervals than the MI.D
and noise multiplication methods with small to moderate ε. In these cases the MI.C methods
also yield larger point estimates of the lognormal mean, lognormal variance, 84th percentile
and 95th percentile in comparison with the other methods. The results of Table 2 are based
25
on a much smaller sample size and here we do not observe such wide confidence intervals
under the MI.C methods.
8. DISCUSSION
How to alter the data before releasing it to the public continues to be a vital concern
of statistical agencies in order to minimize the risk of disclosure. However, this goal has to
be balanced with the interest of preserving the utility of the released data. A number of
strategies exist for achieving the goal of disclosure limitation, and for accurately analyzing the
released data. Perhaps not much effort has been devoted to compare the different disclosure
limitation strategies in terms of accuracy of the inference resulting from the released data.
If a particular data masking approach can provide more accurate inference compared to
other competing approaches, this should be of obvious interest to statistical agencies, survey
organizers, and the public. This work is an attempt in this direction, and our goal has been
two-fold: (a) to develop rigorous data analysis methodologies for noise multiplied data under
noise multiplication of the entire data, or under noise multiplication of the top coded data,
and (b) to compare noise multiplication and multiple imputation in terms of accuracy of
the resulting inference. We have developed all the necessary theoretical results for analyzing
noise multiplied data, when the original (unmasked) sample arises from three parametric
distributions: exponential, normal and lognormal distributions. Masking the entire data, and
masking data above a threshold, are treated separately. As is well known, the latter situation
is very common in the situation of top coding, where sample values above a threshold are
suppressed for privacy protection. We have also reported extensive numerical results to assess
the accuracy of the inference concerning a variety of parameters. The numerical results have
brought out the similarities, differences and advantages of the two data masking techniques
we have investigated.
26
In the top code scenario where only values above a threshold C > 0 require protection,
we have considered noise multiplication under two data release scenarios: case (i) in which
each released value includes an indicator of whether or not it was noise perturbed, and case
(ii) in which no such indicator is provided. We developed data analysis methods under both
cases, and argued that case (i) should always provide more (or equally) accurate inference
than top coding at C, while case (ii) can provide either more or less accurate inference than
top coding at C, depending on the magnitude of the noise variance. Our empirical results
show that both cases provide almost equally accurate inferences when the noise variance
is small, and the difference in accuracy increases, but perhaps is not too substantial, when
the noise variance is moderately large. The case (ii) data release may sometimes be more
desirable for statistical agencies than the case (i) data release, as case (ii) would appear to
provide an enhanced level of protection against disclosure. The results of this article show
how to obtain valid inferences in both cases.
In summary, parametric statistical procedures for fully masked data based on multiple
imputation and noise multiplication can provide comparable inferences in many cases that we
considered. The inferences obtained from these two different methods can usually be made
nearly equivalent by setting the noise variance appropriately. When a large noise variance
providing a high degree of confidentiality is used, inference is typically less accurate but
still reasonable. In the case of top coded data, similar conclusions hold. We note however
that the procedures MI.C90 and MI.C80 do not perform well in most cases as they tend
to produce confidence intervals whose true coverage probability is below the nominal level
even when the sample size is quite large. On the other hand, the methods MI.D90 and
MI.D80 generally do yield satisfactory results, but as noted in Section 6, for smaller sample
sizes, there is a potential for a large RMSE, SD, and wide confidence interval under these
methods. Compared to multiple imputation, an appealing feature of noise multiplication
is its flexibility; the noise variance acts as a tuning parameter, and its choice allows one
27
to balance data quality with confidentiality protection. The results of this article provide
guidance regarding the effect of noise variance on data quality. Our results show, in particular
situations, precisely the value of the noise variance at which noise multiplied data will provide
inferences with nearly equivalent accuracy as synthetic (multiply imputed) data. By setting
the noise variance smaller than this value, we have shown that one can obtain inferences that
are more accurate than synthetic data, but perhaps at the expense of a higher disclosure risk.
Similarly, one can increase the noise variance, decreasing accuracy of inferences, but perhaps
enhancing the level of protection against disclosure. Indeed the impact of the noise variance
on disclosure risk requires further investigation. While inferences become less accurate when
the noise variance is large, we note that the inferences generally are still valid, i.e., confidence
interval coverage probability is generally maintained at the nominal level and bias is small.
28
Table 1. Analysis of household total income with protection for values above C = 90th empiricalpercentile
µ σ2 eµ+σ2/2 e2µ+2σ2 − e2µ+σ2eµ+σ eµ+1.645σ
Est Rel. Est Rel. Est Rel. Est× 10−6 Rel. Est Rel. Est Rel.Len. Len. Len. Len. Len. Len.
CD 10.495 1.000 0.981 1.000 58996 1.000 5805.083 1.000 97263 1.000 184262 1.000MI.C90 10.526 1.049 1.078 1.101 63865 1.156 7903.475 1.447 105220 1.137 205534 1.173MI.C80 10.551 1.075 1.130 1.159 67245 1.262 9478.622 1.798 110648 1.229 219649 1.289MI.D90 10.494 1.000 0.981 1.001 58965 1.001 5793.529 1.000 97212 1.001 184129 1.001MI.D80 10.494 1.001 0.981 1.002 58967 1.003 5795.687 1.002 97215 1.003 184146 1.003CENS 10.510 1.040 1.037 1.140 61592 1.150 6906.667 1.338 101531 1.139 195816 1.178NM10.1 10.495 1.001 0.982 1.002 59048 1.002 5824.788 1.005 97349 1.002 184486 1.003NM10.2 10.495 1.001 0.982 1.002 59051 1.002 5826.076 1.005 97355 1.002 184501 1.003NM20.1 10.496 1.002 0.985 1.006 59169 1.008 5872.738 1.017 97551 1.007 185022 1.009NM20.2 10.496 1.003 0.985 1.007 59200 1.009 5884.083 1.020 97602 1.008 185152 1.010NM30.1 10.497 1.004 0.987 1.012 59293 1.014 5921.903 1.031 97756 1.013 185567 1.017NM30.2 10.497 1.006 0.989 1.015 59384 1.018 5955.307 1.039 97907 1.017 185951 1.021NM40.1 10.497 1.006 0.990 1.019 59420 1.021 5971.468 1.046 97965 1.020 186120 1.025NM40.2 10.499 1.009 0.994 1.025 59639 1.031 6052.017 1.067 98327 1.029 187037 1.036NM50.1 10.499 1.009 0.995 1.028 59650 1.033 6065.054 1.071 98345 1.030 187139 1.038NM50.2 10.502 1.016 1.002 1.042 60084 1.053 6226.125 1.114 99061 1.050 188952 1.061NM60.1 10.499 1.011 0.996 1.034 59685 1.038 6080.100 1.080 98403 1.035 187299 1.044NM60.2 10.505 1.023 1.008 1.058 60404 1.075 6349.797 1.154 99589 1.070 190308 1.085NM70.1 10.501 1.014 1.001 1.045 59942 1.050 6186.262 1.108 98828 1.047 188442 1.059NM70.2 10.510 1.035 1.021 1.086 61117 1.114 6635.825 1.238 100760 1.106 193357 1.129NM80.1 10.502 1.017 1.005 1.053 60128 1.060 6263.484 1.130 99133 1.056 189264 1.070NM80.2 10.515 1.050 1.031 1.114 61707 1.156 6871.419 1.318 101725 1.146 195836 1.175NM90.1 10.502 1.018 1.007 1.060 60221 1.066 6303.106 1.144 99286 1.061 189680 1.078NM90.2 10.518 1.070 1.039 1.141 62177 1.201 7064.943 1.396 102492 1.189 197822 1.223
29
Table 2. Analysis of household alimony payments with protection for values above C = 90thempirical percentile
µ σ2 eµ+σ2/2 e2µ+2σ2 − e2µ+σ2eµ+σ eµ+1.645σ
Est Rel. Est Rel. Est Rel. Est× 10−6 Rel. Est Rel. Est Rel.Len. Len. Len. Len. Len. Len.
CD 8.715 1.000 1.168 1.000 10930 1.000 264.812 1.000 17962 1.000 36069 1.000MI.C90 8.711 1.007 1.183 1.018 10976 1.022 277.204 1.098 18016 1.016 36370 1.025MI.C80 8.725 1.022 1.215 1.049 11337 1.085 314.648 1.320 18574 1.069 37884 1.092MI.D90 8.710 0.994 1.154 0.991 10804 0.985 255.589 0.978 17759 0.986 35529 0.984MI.D80 8.718 1.006 1.179 1.013 11038 1.026 278.497 1.096 18124 1.021 36543 1.028CENS 8.740 1.055 1.277 1.181 11829 1.224 361.734 1.574 19338 1.192 40082 1.251NM10.1 8.715 1.000 1.168 1.000 10922 0.999 264.096 0.998 17949 0.999 36034 0.999NM10.2 8.715 1.000 1.169 1.001 10934 1.001 265.245 1.003 17969 1.001 36088 1.002NM20.1 8.715 1.000 1.168 1.002 10930 1.002 264.725 1.002 17962 1.002 36066 1.002NM20.2 8.715 1.000 1.168 1.003 10930 1.002 264.783 1.003 17962 1.002 36069 1.003NM30.1 8.719 1.007 1.182 1.017 11046 1.023 275.907 1.056 18142 1.020 36581 1.025NM30.2 8.719 1.007 1.182 1.018 11042 1.023 275.624 1.056 18137 1.021 36567 1.026NM40.1 8.719 1.007 1.182 1.020 11047 1.026 276.037 1.060 18143 1.023 36586 1.029NM40.2 8.717 1.005 1.176 1.016 10990 1.019 270.739 1.038 18055 1.017 36340 1.021NM50.1 8.724 1.017 1.203 1.043 11219 1.059 293.152 1.145 18411 1.051 37349 1.065NM50.2 8.721 1.014 1.193 1.039 11130 1.048 284.737 1.111 18272 1.043 36967 1.054NM60.1 8.724 1.019 1.207 1.051 11246 1.067 296.198 1.165 18451 1.058 37474 1.075NM60.2 8.720 1.018 1.200 1.054 11165 1.064 289.284 1.145 18324 1.056 37144 1.072NM70.1 8.725 1.019 1.206 1.055 11246 1.070 296.116 1.169 18452 1.061 37472 1.078NM70.2 8.714 1.013 1.181 1.047 10985 1.045 272.534 1.080 18043 1.041 36371 1.053NM80.1 8.725 1.021 1.207 1.063 11252 1.078 296.798 1.182 18461 1.068 37501 1.087NM80.2 8.726 1.032 1.215 1.093 11315 1.117 303.461 1.249 18558 1.104 37783 1.130NM90.1 8.724 1.019 1.203 1.059 11217 1.071 293.298 1.164 18407 1.063 37348 1.080NM90.2 8.687 1.003 1.134 1.034 10449 0.999 230.225 0.922 17191 1.004 34168 1.005
30
SUPPLEMENTARY MATERIALS
The supplementary material consists of five appendices as follows.
Appendix B: MLEs and Fisher information under full noise multiplication.
Appendix C: MLEs and Fisher information under noise multiplication of extreme values.
Appendix D: MLEs and Fisher information under top coding.
Appendix E: Simulation results.
Appendix F: Analysis of fully masked data on total household income and household al-
imony payment based on data from the 2000 U.S. Current Population Survey.
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34
APPENDIX A: PROOF OF PROPOSITION 1 AND SOME RELATED RESULTS
We let Y ∼ fθ(y), independent of R ∼ h(r), as defined in Section 2 and we let ∆ = I(Y ≤ C),
X = Y if Y ≤ C and = R× Y if Y > C, as defined in Section 3, where C > 0 is a constant.
Then letting Fθ(y) =∫ y−∞ fθ(t)dt and H(r) =
∫ r0h(t)dt, we have, for r > 0,
Pr(X ≤ x,R ≤ r,∆ = 1) = Pr(X ≤ x,R ≤ r |∆ = 1) Pr(∆ = 1)
= Pr(Y ≤ x,R ≤ r |Y ≤ C)P (Y ≤ C)
= Pr(Y ≤ x, Y ≤ C,R ≤ r)
=
Fθ(x)H(r), if x ≤ C,
Fθ(C)H(r), if x > C,(10)
and, for r > 0, C > 0,
Pr(X ≤ x,R ≤ r,∆ = 0) = Pr(X ≤ x,R ≤ r |∆ = 0) Pr(∆ = 0)
= Pr(Y R ≤ x,R ≤ r |Y > C) Pr(Y > C)
= Pr(Y R ≤ x, Y > C,R ≤ r)
= Pr(C < Y ≤ x
R,R ≤ r)
=
∫ r
0
∫ x/ωC
fθ(y)h(ω)dydω, if r ≤ xC,∫ x/C
0
∫ x/ωC
fθ(y)h(ω)dydω, if r > xC> 0,
0, if x ≤ 0,
=
∫ r
0[Fθ(x/ω)− Fθ(C)]h(ω)dω, if r ≤ x
C,∫ x/C
0[Fθ(x/ω)− Fθ(C)]h(ω)dω, if 0 < x
C< r,
0, if x ≤ 0.
(11)
35
To obtain the joint pdf of (X,R,∆), we differentiate (10) and (11) with respect to x and r
to obtain:
∂2
∂x∂rPr(X ≤ x,R ≤ r,∆ = 1) =
fθ(x)h(r), if x < C,
0, if x > C,(12)
∂2
∂x∂rPr(X ≤ x,R ≤ r,∆ = 0) =
fθ(x/r)h(r)(1/r), if r < x
C,
0, if 0 < xC< r,
0, if x < 0,
(13)
which completes the proof of Proposition 1. Letting (x1,∆1), ...., (xn,∆n) be iid as (X,∆),
the following results then follow from Proposition 1.
Result 1. The joint pdf of (X,∆) is given by
kθ(x, δ) =
fθ(x), if x < C, δ = 1,
0, if xi > C, δ = 1,∫ x/C0
fθ(x/r)h(r)(1/r)dr, if x > 0, δ = 0,
0, if x < 0, δ = 0.
(14)
Result 2. The likelihood function for θ based on (x1,∆1), ...., (xn,∆n) is given by
L(θ|x1, ...., xn,∆1, ....,∆n) =n∏i=1
kθ(xi,∆i)
=n∏i=1
{[fθ(xi)]∆i × [
∫ xi/C
0
fθ(xi/r)h(r)(1/r)dr]1−∆i}. (15)
36
Result 3. The marginal pdf of X is given by
kθ(x) = fθ(x)I(x < C) +
∫ x/C
0
fθ(x/r)h(r)(1/r)drI(x > 0) (16)
=
fθ(x) +
∫ x/C0
fθ(x/r)h(r)(1/r)dr, if 0 < x < C,
fθ(x), if x < 0,∫ x/C0
fθ(x/r)h(r)(1/r)dr, if x > C.
Result 4. The likelihood function for θ based on x1, ...., xn is given by
L(θ|x1, ...., xn) =n∏i=1
kθ(xi)
=n∏i=1
{fθ(xi)I(xi < C) +
∫ xi/C
0
fθ(xi/r)h(r)(1/r)drI(xi > 0)}. (17)
37
SUPPLEMENTARY MATERIAL
A Comparison of Statistical Disclosure Control Methods:Multiple Imputation Versus Noise Multiplication
Martin Klein, Thomas Mathew, and Bimal Sinha
APPENDIX B: MLEs AND FISHER INFORMATION UNDER FULL NOISEMULTIPLICATION
B.1 Exponential distributionWe assume Y ∼ fθ(y) = 1
θe− yθ , 0 < y < ∞. Then the joint pdf g(z, r) of (Z,R), the marginal
pdf g(z) of Z and the conditional pdf g(r|z) of R, given Z = z, are given by
gθ(z, r) =1
θe−
zrθh(r)
r, gθ(z) =
∫ ∞0
1
θe−
zrθh(r)
rdr, gθ(r|z) =
e−zrθh(r)r∫∞
0 e−zwθ
h(w)w dw
, (1)
for 0 < r < ∞ and 0 < z < ∞, and hence the complete data likelihood L(θ|uc) and loglikelihood`(θ|uc) can be expressed as
L(θ|uc) ∼1
θne− 1θ
∑ni=1
ziri , `(θ|uc) = −n ln θ − 1
θ
n∑i=1
ziri. (2)
The E and M -steps for computing the MLE of θ based on z are as follows.E-step.
Q(θ|θ(t)) = Eθ(t) [`(θ|uc)|uobs] = −n ln θ − 1
θ
n∑i=1
ziE[1
ri|zi] (3)
M-step. Obviously Q(θ|θ(t)) is maximized with respect to θ at θ = 1n
∑ni=1 ziψ(θ(t), zi) where
ψ(θ(t), zi) = Eθ(t) [1ri|zi].
Thus the EM iterations are defined by
θ(t+1) =1
n
n∑i=1
ziψ(θ(t), zi). (4)
The computation of ψ(θ(t), z) for any z follows directly from the conditional pdf of r, given z, whichis given by (1).
In the special case when R ∼ Uniform(1− ε, 1 + ε), upon direct integration, ψ(θ(t), z) simplifiesto
ψuniform(θ(t), z) =
θ(t)
z
[e− z
θ(t)(1+ε) − e− z
θ(t)(1−ε)
]∫ 1+ε
1−ε e− z
wθ(t)dww
. (5)
38
Lastly, the observed Fisher information is computed by adding component-wise terms based onz1, . . . , zn, with a generic term as follows. Since the marginal pdf of z is given by (1), we get thefirst two derivatives of ln[gθ(z)] as
∂ ln[gθ(z)]
∂θ= −1
θ+
∫∞0 e−
zrθzh(r)r2θ2
dr∫∞0 e−
zrθh(r)r dr
, (6)
∂2 ln[gθ(z)]
∂θ2=
1
θ2− 2z
θ3
∫∞0 e−
zrθh(r)r2dr∫∞
0 e−zrθh(r)r dr
+z2
θ4
∫∞0 e−
zrθh(r)r3dr∫∞
0 e−zrθh(r)r dr
− z2
θ4
[∫∞0 e−
zrθh(r)r2dr∫∞
0 e−zrθh(r)r dr
]2
. (7)
A remark is now in order. Since the choice of the noise distribution mostly relies on the dataanalyst, a special case leading to simplified inferential methods warrants some attention. We referto this as a customized or conjugate noise distribution. We choose
R ∼ hδ(r) =δδ+1
Γ(δ + 1)r−δ−2e−
δr , δ > 1. (8)
It is easy to verify that E(R) = 1, as desired, and var(R) = σ2r = 1
δ−1 . We choose δ > 1 for adesirable level of noise variation. A direct computation shows that the pdf of Z = Y ×R is obtainedas
gθ(z) =δ + 1
θ× δδ+1
( zθ + δ)δ+2. (9)
This readily leads to the following likelihood based on z1, ...., zn:
L(θ|uobs) ∼ θ−n ×n∏i=1
(ziθ
+ δ)−δ−2. (10)
The maximum likelihood estimate of θ in this case can be directly computed by solving the equation:
d`(θ|uobs)
dθ= −n
θ+δ + 2
θ2
n∑i=1
zi( ziθ + δ)
= 0, (11)
which can be simplified asn∑i=1
zizi + θδ
=n
δ + 2. (12)
To compute the observed Fisher information about θ contained in the data uobs, we note that uponsimplification,
−d2`(θ|uobs)
dθ2=n(δ + 1)
θ2− δ2(δ + 2)
n∑i=1
1
(zi + θδ)2. (13)
39
B.2 Normal distribution
We assume Y ∼ fθ(y) ∼ 1σe− (y−µ)2
2σ2 , θ = (µ, σ2). Then the joint pdf g(z, r) of (Z,R), themarginal pdf g(z) of Z and the conditional pdf g(r|z) of R, given Z = z, are given by
gθ(z, r) ∼1
σe−
( zr−µ)2
2σ2h(r)
r, gθ(z) ∼
1
σ
∫ ∞0
e−( zr−µ)
2
2σ2h(r)
rdr, gθ(r|z) =
e−( zr−µ)
2
2σ2h(r)r∫∞
0 e−( zr−µ)
2
2σ2h(r)r dr
, (14)
for 0 < r < ∞ and 0 < z < ∞, and hence the complete data likelihood L(θ|uc) and loglikelihood`(θ|uc) are now expressed as
L(θ|uc) ∼1
σne− 1
2σ2
∑ni=1(
ziri−µ)2
, `(θ|uc) = −n lnσ − 1
2σ2
n∑i=1
(ziri− µ)2. (15)
The EM steps for computing the MLE of θ based on z are as follows.E-step. We compute
Q(θ|θ(t)) = Eθ(t) [`(θ|uc)|uobs],
= −n lnσ − 1
2σ2
n∑i=1
[z2i ψ2(θ(t), zi)− 2µziψ1(θ(t), zi) + µ2], (16)
where ψ1(θ(t), zi) = Eθ(t) [1ri|zi] and ψ2(θ(t), zi) = Eθ(t) [
1r2i|zi], and these two quantities can be readily
computed based on g(r|z) given in (14).M-step. Note that
∂Q(θ|θ(t))
∂µ=
1
σ2
n∑i=1
ziψ1(θ(t), zi)−nµ
σ2,
∂Q(θ|θ(t))
∂σ2= − n
2σ2+
1
2σ4
n∑i=1
[z2i ψ2(θ(t), zi)− 2µziψ1(θ(t), zi) + µ2
]. (17)
Hence Q(θ|θ(t)) is maximized at
µ =1
n
n∑i=1
ziψ1(θ(t), zi), σ2 =1
n
n∑i=1
z2i ψ2(θ(t), zi)− (µ)2. (18)
Thus the EM iterations are defined by
µ(t+1) =1
n
n∑i=1
ziψ1(θ(t), zi), [σ(t+1)]2 =1
n
n∑i=1
z2i ψ2(θ(t), zi)− [µ(t+1)]2. (19)
The observed Fisher information is computed by adding component-wise terms based on z1, ...., zn.A generic term can be obtained as follows. We note that the marginal pdf of Z is given by
gθ(z) ∼1
σ
∫ ∞0
e−( zr−µ)
2
2σ2h(r)
rdr. (20)
40
Writing the integrand above as gθ(z, r), we get
∂gθ(z)
∂µ=
∫ ∞0
gθ(z, r)[( zr − µ)
σ2]dr =
1
σ2
[∫ ∞0
gθ(z, r)z
rdr − µgθ(z)
], (21)
resulting in∂ ln gθ(z)
∂µ=
1
σ2
[∫∞0 gθ(z, r)
zrdr
gθ(z)− µg(z)
], (22)
and hence in∂2 ln gθ(z)
∂µ2=
1
σ2
∂
∂µ
[∫∞0 gθ(z, r)
zrdr
gθ(z)
]− 1
σ2. (23)
Note that
∂
∂µ
[∫∞0 gθ(z, r)
zrdr
gθ(z)
]=
∂∂µ
∫∞0 gθ(z, r)
zrdr
gθ(z)−
[∫∞
0 gθ(z, r)zrdr][
∂gθ(z)∂µ ]
g2θ(z)
. (24)
Since
∂
∂µ
∫ ∞0
gθ(z, r)z
rdr =
∫ ∞0
gθ(z, r)z
r(z
r− µ)
1
σ2dr
=z2
σ2
∫ ∞0
gθ(z, r)dr
r2− zµ
σ2
∫ ∞0
gθ(z, r)dr
r, (25)
upon using (23) and simplifying, we get
∂2 ln gθ(z)
∂µ2=
z2
σ4gθ(z)
[∫ ∞0
gθ(z, r)dr
r2−
(∫∞
0 gθ(z, r)drr )2
gθ(z)
]− 1
σ2. (26)
We next compute ∂gθ(z)∂σ2 which easily simplifies to
∂gθ(z)
∂σ2= − 1
2σ2gθ(z) +
1
2σ4
∫ ∞0
gθ(z, r)(z
r− µ)2dr, (27)
and readily leads to∂ ln gθ(z)
∂σ2=
1
2σ4
∫∞0 gθ(z, r)(
zr − µ)2dr
gθ(z)− 1
2σ2. (28)
Keeping aside the last term, the partial derivative of the first term again with respect to σ2 isobtained as
∂
∂σ2
[1
2σ4
∫∞0 gθ(z, r)(
zr − µ)2dr
gθ(z)
]= − 1
σ6
∫∞0 gθ(z, r)(
zr − µ)2dr
gθ(z)
+1
2σ4
∫∞0
∂∂σ2 gθ(z, r)(
zr − µ)2dr
gθ(z)
− 1
2σ4
∫∞0 gθ(z, r)(
zr − µ)2dr × ∂
∂σ2 gθ(z)
g2θ(z)
. (29)
41
Using the expressions for ∂∂σ2 gθ(z, r) and ∂
∂σ2 gθ(z) given above in (27) and simplifying, we get
∂2
(∂σ2)2ln gθ(z) = − 1
σ6
∫∞0 gθ(z, r)(
zr − µ)2dr
gθ(z)+
1
4σ8
∫∞0 gθ(z, r)(
zr − µ)4dr
gθ(z)
− 1
4σ8[
∫∞0 gθ(z, r)(
zr − µ)2dr
gθ(z)]2 +
1
2σ4. (30)
Finally, we compute ∂2
∂µ∂σ2 [ln gθ(z)]. Recalling (28), we can write
∂2
∂µ∂σ2[ln gθ(z)] =
∂
∂µ
[1
2σ4
∫∞0 gθ(z, r)(
zr − µ)2dr
gθ(z)
]=
1
2σ4gθ(z)
[−2
∫ ∞0
gθ(z, r)(z
r− µ)dr +
1
σ2
∫ ∞0
gθ(z, r)(z
r− µ)3dr
]− 1
2σ6
[∫∞0 gθ(z, r)(
zr − µ)dr][
∫∞0 gθ(z, r)(
zr − µ)2dr
]g2θ(z)
= − 1
σ4
∫∞0 gθ(z, r)(
zr − µ)dr
gθ(z)+
1
2σ6
∫∞0 gθ(z, r)(
zr − µ)3dr
gθ(z)
− 1
2σ6
[∫∞
0 gθ(z, r)(zr − µ)dr][
∫∞0 gθ(z, r)(
zr − µ)2dr]
g2θ(z)
. (31)
B.3 Lognormal distribution
We assume Y ∼ fθ(y) ∼ 1yσe− (ln y−µ)2
2σ2 , 0 < y < ∞, and θ = (µ, σ2). Then the joint pdf g(z, r)of (Z,R), the marginal pdf g(z) of Z and the conditional pdf g(r|z) of R, given Z = z, are givenby
gθ(z, r) ∼1
zσe−
(ln z−ln r−µ)2
2σ2 h(r),
gθ(z) ∼1
zσ
∫ ∞0
e−ln z−ln r−µ)2
2σ2 h(r)dr, (32)
gθ(r|z) =e−
(ln z−ln r−µ)2
2σ2 h(r)∫∞0 e−
(ln z−ln r−µ)22σ2
h(r)dr, (33)
for 0 < r < ∞ and 0 < z < ∞, and hence the complete data likelihood and log-likelihood can beexpressed as
L(θ|zc) ∼1
σne− 1
2σ2
∑ni=1(ln
ziri−µ)2
, (34)
`(θ|uc) = −n lnσ − 1
2σ2
n∑i=1
(lnziri− µ)2 (35)
= −n lnσ − 1
2σ2
n∑i=1
(lnziri
)2 +µ
σ2
n∑i=1
lnziri− nµ2
2σ2.
42
The EM steps for computing the MLE of θ based on z are as follows.E-step. We compute
Q(θ|θ(t)) = Eθ(t) [`(θ|uc)|uobs]
= −n lnσ − 1
2σ2
n∑i=1
[ψ2(θ(t), zi) +µ
σ2ψ1(θ(t), zi)]−
nµ2
2σ2, (36)
where ψ1(θ(t), zi) = Eθ(t) [lnziri|zi] and ψ2(θ(t), zi) = Eθ(t) [(ln
ziri
)2|zi], and these two quantities canbe readily computed based on the conditional pdf of R, given z, mentioned in (33).M-step. We note that
∂Q(θ|θ(t))
∂µ=
1
σ2
n∑i=1
ψ1(θ(t), zi)−nµ
σ2= 0
yields µ = 1n
∑ni=1 ψ1(θ(t), zi), and,
∂Q(θ|θ(t))
∂σ2= − n
2σ2+
1
2σ4
n∑i=1
ψ2(θ(t), zi)−µ
σ4
n∑i=1
ψ1(θ(t), zi) +nµ2
2σ4= 0
yields σ2 = 1n
∑ni=1 ψ2(θ(t), zi)− µ2. Thus the EM iterations are defined by
µ(t+1) =1
n
n∑i=1
ψ1(θ(t), zi), (σ(t+1))2 =1
n
n∑i=1
ψ2(θ(t), zi)− (µ(t+1))2. (37)
The observed Fisher information is computed by adding component-wise terms based on z1, ...., zn,with a generic term as follows. Since the marginal pdf of Z is given by (32), we obtain,
∂ ln gθ(z)
∂µ=
∫∞0 e−
(ln z−ln r−µ)2
2σ2ln z−ln r−µ
σ2 h(r)dr∫∞0 e−
(ln z−ln r−µ)22σ2 h(r)dr
, (38)
∂2 ln gθ(z)
∂µ2= − 1
σ2+
∫∞0 e−
(ln z−ln r−µ)2
2σ2 ( ln z−ln r−µσ2 )2h(r)dr∫∞
0 e−(ln z−ln r−µ)2
2σ2 h(r)dr
−
∫∞0 e−(ln z−ln r−µ)2
2σ2ln z−ln r−µ
σ2 h(r)dr∫∞0 e−
(ln z−ln r−µ)22σ2 h(r)dr
2
, (39)
43
and
∂2 ln gθ(z)
∂µ∂σ2= − 1
σ4×∫∞
0 e−(ln z−ln r−µ)2
2σ2 (ln z − ln r − µ)h(r)dr∫∞0 e−
(ln z−ln r−µ)22σ2 h(r)dr
+1
2σ6×∫∞
0 e−(ln z−ln r−µ)2
2σ2 (ln z − ln r − µ)3h(r)dr∫∞0 e−
(ln z−ln r−µ)22σ2 h(r)dr
− 1
2σ6
[∫∞0 e−
(ln z−ln r−µ)2
2σ2 (ln z − ln r − µ)h(r)dr ×∫∞
0 e−(ln z−ln r−µ)2
2σ2 (ln(z/r)− µ)2h(r)dr
][∫∞
0 e−(ln(z/r)−µ)2
2σ2 h(r)dr
]2 .
(40)
Finally, we get
∂ ln gθ(z)
∂σ2= − 1
2σ2+
1
2σ4
∫∞0 e−
(ln z−ln r−µ)2
2σ2 (ln z − ln r − µ)2h(r)dr∫∞0 e−
(ln z−ln r−µ)22σ2 h(r)dr
,
∂2 ln gθ(z)
(∂σ2)2=
1
2σ4+
1
σ6
∫∞0 e−
(ln z−ln r−µ)2
2σ2 (ln z − ln r − µ)2h(r)dr∫∞0 e−
(ln z−ln r−µ)22σ2 h(r)dr
+1
4σ8
∫∞0 e−
(ln z−ln r−µ)2
2σ2 (ln z − ln r − µ)4h(r)dr∫∞0 e−
(ln z−ln r−µ)22σ2 h(r)dr
− 1
4σ8
∫∞0 e−(ln z−ln r−µ)2
2σ2 (ln z − ln r − µ)2h(r)dr∫∞0 e−
(ln z−ln r−µ)22σ2 h(r)dr
2
. (41)
A customized or conjugate noise distribution is obtained as follows. Since Y follows a lognormaldistribution, implying lnY ∼ N(µ, σ2) and since Z = Y × R, we choose R ∼ lognormal with
lnR ∼ N(−ψ2
2 , ψ2). Then E(R) = 1 and var(R) = σ2
r = eψ2 − 1. This readily yields
lnZ ∼ N(µ− ψ2
2= µz, σ
2 + ψ2 = σ2z) (42)
Since µz = 1n
∑ni=1 ln zi and σ2
z = 1n
∑ni=1(ln zi − µz)2, we obtain µ = µz + ψ2
2 and σ2 = σ2z − ψ2.
Since the estimated variance-covariance matrix of (µz, σ2z) readily follows from the observed Fisher
information matrix for (µz, σ2z) given by
Iobs(µz, σ2z) =
(nσ2z
0
0 n2σ4z
). (43)
The estimated variances of meaningful and useful functions g(., .) of µz and σ2z can be easily obtained
by computing the required partial derivatives. We provide below examples of such functions.
44
1. g(µz, σ2z) = eµ+σ2
2 = eµz+ψ2
2 .
2. g(µz, σ2z) = e2µ+2σ2 − e2µ+σ2
= e2µz+2σ2z−ψ2 − e2µz+σ2
z .
3. g(µz, σ2z) = eµ+cσ = eµz+ψ2
2+c(σ2
z−ψ2)12 .
Note that the first and second functions are, respectively, the mean and variance of the originallognormal random variable Y , expressed in terms of the mean and variance of the random variablelnZ, specified in (42). Similarly, the third function is a percentile of Y . Recall once again thatdata are not available on Y , but observations are available on the perturbed quantity Z. In otherwords, inference on the above functions related to the distribution of Y can now be carried outusing the data on Z.
45
APPENDIX C: MLEs AND FISHER INFORMATION UNDER NOISE MULTIPLICATION OFEXTREME VALUES
Here we present details concerning the computation of the MLEs, and derivation of the Fisherinformation matrices in the context of the exponential, normal and lognormal distributions. Theseare required for the data analysis presented in Section 3 of the paper, dealing with noise multi-plication of the extreme values in the sample. In what follows, the notations used are as given inSection 3 of the paper.
C1. Exponential distributionWe consider the case of Y ∼ fθ(y) = 1
θe−y/θ, 0 < y <∞. Then the complete data log-likelihood
function can be expressed as
`(θ|y) = −n ln θ − 1
θ
n∑i=1
[∆ixi + (1−∆i)xiri
]. (44)
Case (i). We now describe the EM algorithm for computing the MLE of θ based on the data vi,obs.
E-step.
Q(θ|θ(t)) = Eθ(t) [`(θ|vc)|vi,obs]
= −n ln θ − 1
θ
n∑i=1
{∆ixi + (1−∆i)xiEθ(t)
[r−1i |xi,∆i = 0
]}where
Eθ(t)[r−1i |xi,∆i = 0
]=
∫ xi/C0 exp
(− 1θ(t)
xir
)h(r)r−2dr∫ xi/C
0 exp(− 1θ(t)
xiω
)h(ω)ω−1dω
.
M-step. The value of θ that maximizes Q(θ|θ(t)) is readily computed, thus the following equationdefines the sequence of EM iterations:
θ(t+1) =1
n
n∑i=1
{∆ixi + (1−∆i)xiEθ(t)
[r−1i |xi,∆i = 0
]}(45)
with the expression for Eθ(t) [r−1i |xi,∆i = 0] as given above.
From Result 2 in Appendix A of the paper, the loglikelihood is
`(θ|x1, . . . , xn,∆1, . . . ,∆n) = −n ln θ − 1
θ
n∑i=1
xi∆i +
n∑i=1
(1−∆i) ln[
∫ x/C
0exp(−xi
rθ)h(r)r−1dr],
and hence the observed Fisher information is readily obtained based on the following:
∂2l(θ|x1, . . . , xn,∆1, . . . ,∆n)
∂θ2=
n
θ2− 2
θ3
n∑i=1
xi∆i −2
θ3
n∑i=1
(1−∆i)xi
∫ xi/C0 e−
xirθh(r)r2dr∫ xi/C
0 e−xirθh(r)r dr
+1
θ4
n∑i=1
(1−∆i)x2i
∫ xi/C0 e−
xirθh(r)r3dr∫ xi/C
0 e−xirθh(r)r dr
− 1
θ4
n∑i=1
(1−∆i)x2i [
∫ xi/C0 e−
xirθh(r)r2dr∫ xi/C
0 e−xirθh(r)r dr
]2. (46)
46
Case (ii). We now describe the EM algorithm for computing the MLE of θ based on the datavii,obs.E-step.
Q(θ|θ(t)) = Eθ(t) [`(θ|vc)|vii,obs]
= −n ln θ − 1
θ
n∑i=1
{xiEθ(t) [∆i|xi] + xiEθ(t) [(1−∆i)r
−1i |xi]
},
where
Eθ(t) [∆i|xi] =I(xi < C) exp
[−xi/θ(t)
]I(xi < C) exp
[−xi/θ(t)
]+∫ xi/C
0 exp[− 1θ(t)
xiω
]h(ω)ω−1dω
,
and
Eθ(t) [(1−∆i)r−1i |xi] =
∫ xi/C0 exp
[− 1θ(t)
xiri
]h(ri)r
−2i dri
I(xi < C) exp[−xi/θ(t)
]+∫ xi/C
0 exp[− 1θ(t)
xiω
]h(ω)ω−1dω
.
M-step. Maximization of Q(θ|θ(t)) with respect to θ is readily accomplished, and hence we obtainthe following equation which defines the sequence of EM iterations:
θ(t+1) =1
n
n∑i=1
{xiEθ(t) [∆i|xi] + xiEθ(t) [(1−∆i)r
−1i |xi]
}, (47)
where the expressions for Eθ(t) [∆i|xi] and Eθ(t) [(1−∆i)r−1i |xi] are given above.
Recalling Result 4 given in Appendix A of the paper, the observed Fisher information in thiscase is based on the loglikelihood
`(θ|x1, . . . , xn) = −n ln θ +n∑i=1
ln[e−xiθ I(xi < C) +
∫ xiC
0e−
xirθh(r)
rdr] (48)
This gives
∂l(θ|x1, . . . , xn)
∂θ= −n
θ+
1
θ2
n∑i=1
xi[e−
xiθ I(xi < C) +
∫ xiC
0 e−xirθh(r)r2dr
kθ(xi)]. (49)
Hence we get
∂2l(θ|x1, . . . , xn)
∂θ2=
n
θ2− 2
θ3
n∑i=1
xi[e−
xiθ I(xi < C) +
∫ xiC
0 e−xirθh(r)r2dr
kθ(xi)]
+1
θ4
n∑i=1
x2i [e−
xiθ I(xi < C) +
∫ xiC
0 e−xirθh(r)r3dr
kθ(xi)]
− 1
θ4
n∑i=1
x2i [e−
xiθ I(xi < C) +
∫ xiC
0 e−xirθh(r)r2dr
kθ(xi)]2. (50)
47
C2. Normal distributionWe next consider the case Y ∼ fθ(y) = 1√
2πσ2exp
[− (y−µ)2
2σ2
], −∞ < y <∞, where θ = (µ, σ2).
Then the complete data likelihood function is
L(θ|vc) =n∏i=1
{1√
2πσ2exp
[−(xi − µ)2
2σ2
]}∆i{
1√2πσ2
exp
[−(xiri − µ)2
2σ2
]}1−∆i
∝n∏i=1
{1√σ2
exp
[−(xi − µ)2
2σ2
]}∆i{
1√σ2
exp
[−
(xiri − µ)2
2σ2
]}1−∆i
= (σ2)−n/2n∏i=1
{exp
[−(xi − µ)2
2σ2
]}∆i{
exp
[−
(xiri − µ)2
2σ2
]}1−∆i
,
and hence we get the complete data log-likelihood function as
`(θ|vc) = −n2
ln(σ2)− 1
2σ2
n∑i=1
{∆i(xi − µ)2 + (1−∆i)
(xiri− µ
)2}
= −n2
ln(σ2)− nµ2
2σ2− 1
2σ2
n∑i=1
{∆i
[(xi)
2 − 2µxi]
+ (1−∆i)
[(xiri
)2 − 2µxiri
]}.
Case (i). The EM algorithm for computing the MLE of θ based on (x1,∆1), . . . , (xn,∆n) is asfollows.
E-step.
Q(θ|θ(t)) = Eθ(t) [`(θ|vc)|vi,obs] = −n2
ln(σ2)− nµ2
2σ2− 1
2σ2
n∑i=1
{∆i[(xi)
2 − 2µxi]}
− 1
2σ2
n∑i=1
{(1−∆i)(Eθ(t) [(xiri
)2|xi,∆i = 0]− 2µEθ(t) [(xiri
)|xi,∆i = 0])}
where
Eθ(t)
[(xiri
)2|xi,∆i = 0
]= x2
i
∫ xi/C0 exp
[− (xi/r)−µ(t)}2
2(σ(t))2
]h(r)r3dr∫ xi/C
0 exp[− (xi/ω)−µ(t)}2
2(σ(t))2
]h(ω)ω dω
≡ x2iψ1(θ(t), xi),
Eθ(t)
[(xiri
)|xi,∆i = 0
]= xi
∫ xi/C0 exp
[− (xi/r)−µ(t)}2
2(σ(t))2
]h(r)r2dr∫ xi/C
0 exp[− (xi/ω)−µ(t)}2
2(σ(t))2
]h(ω)ω dω
≡ xiψ2(θ(t), xi).
M-step. By maximizing Q(θ|θ(t)) with respect to θ, we obtain the following equations which definethe sequence of EM iterations:
µ(t+1) =1
n
n∑i=1
{∆ixi + (1−∆i)xiψ2(θ(t), xi)
},
(σ(t+1))2 =1
n
(n∑i=1
{∆i(xi)
2 + (1−∆i)x2iψ1(θ(t), xi)
})− (µ(t+1))2,
48
where the expressions for ψ1(θ(t), xi) and ψ2(θ(t), xi) are given above. When ∆i = 1, ψ1(θ(t), xi)and ψ2(θ(t), xi) are defined as equal to 0.
To compute the observed Fisher information, note that the loglikelihood based on one observa-tion x can be expressed as
`(θ|x,∆) = lnL(θ|x,∆) ∼ −1
2ln(σ2)− 1
2σ2∆(x−µ)2 + (1−∆) ln
[∫ xC
0e−
12σ2
(xr−µ)2 h(r)
rdr
]. (51)
This yields
∂`(θ|x,∆)
∂µ=
∆(x− µ)
σ2+
(1−∆)
σ2
[∫ xC
0 e−1
2σ2(xr−µ)2(xr − µ)h(r)
r dr∫ xC
0 e−1
2σ2(xr−µ)2 h(r)
r dr
]
=∆(x− µ)
σ2− µ(1−∆)
σ2+
(1−∆)
σ2
[∫ xC
0 e−1
2σ2(xr−µ)2(xr )h(r)
r dr∫ xC
0 e−1
2σ2(xr−µ)2 h(r)
r dr
]. (52)
Hence we get
∂2`(θ|x,∆)
∂µ2= − 1
σ2+
(1−∆)
σ4
[∫ xC
0 e−1
2σ2(xr−µ)2(xr − µ)(xr )h(r)
r dr∫ xC
0 e−1
2σ2(xr−µ)2 h(r)
r dr
−(∫ xC
0 e−1
2σ2(xr−µ)2(xr − µ)h(r)
r dr)(∫ xC
0 e−1
2σ2(xr−µ)2(xr )h(r)
r dr)
(∫ xC
0 e−1
2σ2(xr−µ)2 h(r)
r dr)2
]. (53)
From (52), we get
∂2`(θ|x,∆)
∂µ∂σ2= −x∆− µ
σ4− (1−∆)
σ4[
∫ xC
0 e−1
2σ2(xr−µ)2(xr )h(r)
r dr∫ xC
0 e−1
2σ2(xr−µ)2 h(r)
r dr]
+(1−∆)
2σ6
[∫ xC
0 e−1
2σ2(xr−µ)2(xr − µ)2(xr )h(r)
r dr∫ xC
0 e−1
2σ2(xr−µ)2 h(r)
r dr
−(∫ xC
0 e−1
2σ2(xr−µ)2(xr − µ)2 h(r)
r dr)(∫ xC
0 e−1
2σ2(xr−µ)2(xr )h(r)
r dr)
(∫ xC
0 e−1
2σ2(xr−µ)2 h(r)
r dr)2
]. (54)
Lastly, we note that
∂`(θ|x,∆)
∂σ2= − 1
2σ2+
∆(x− µ)2
2σ4+
(1−∆)
2σ4
[∫ xC
0 e−1
2σ2(xr−µ)2(xr − µ)2 h(r)
r dr∫ xC
0 e−1
2σ2(xr−µ)2 h(r)
r dr
]. (55)
Hence we get
∂2`(θ|x,∆)
∂(σ2)2=
1
2σ4− ∆(x− µ)2
σ6− (1−∆)
σ6
[∫ xC
0 e−1
2σ2(xr−µ)2(xr − µ)2 h(r)
r dr∫ xC
0 e−1
2σ2(xr−µ)2 h(r)
r dr
]
+(1−∆)
4σ8
[∫ xC
0 e−1
2σ2(xr−µ)2(xr − µ)4 h(r)
r dr∫ xC
0 e−1
2σ2(xr−µ)2 h(r)
r dr− (
∫ xC
0 e−1
2σ2(xr−µ)2(xr − µ)2 h(r)
r dr∫ xC
0 e−1
2σ2(xr−µ)2 h(r)
r dr)2
]. (56)
49
Case (ii). The EM algorithm for computing the MLE of θ based on (x1, . . . , xn) is as follows.
E-step.
Q(θ|θ(t)) = Eθ(t) [`(θ|vc)|vii,obs]
= −n2
ln(σ2)− nµ2
2σ2− 1
2σ2
n∑i=1
{(xi)
2 − 2µxi}Eθ(t) [∆i|xi]}
− 1
2σ2
n∑i=1
{Eθ(t) [(1−∆i)(
xiri
)2|xi]− 2µEθ(t) [(1−∆i)(xiri
)|xi]}
where
Eθ(t) [∆i|xi] =I(xi < C) exp
[− (xi−µ(t))2
2(σ(t))2
]I(xi < C) exp
[− (xi−µ(t))2
2(σ(t))2
]+∫ xi/C
0 exp[−{(xi/ω)−µ(t)}2
2(σ(t))2
]h(ω)ω dω
≡ ψ1(θ(t), xi).
Eθ(t) [(1−∆i)(xiri
)2|xi] = x2i
∫ xi/C0 exp
[−{ln(xi/r)−µ(t)}2
2(σ(t))2
]h(r)r3dr
I(xi < C) exp[−{xi−µ
(t)}22(σ(t))2
]+∫ xi/C
0 exp[−{(xi/ω)−µ(t)}2
2(σ(t))2
]h(ω)ω dω
≡ x2iψ2(θ(t), xi).
Eθ(t) [(1−∆i)(xiri
)|xi] = xi
∫ xi/C0 (xir ) exp
[−{(xi/r)−µ
(t)}22(σ(t))2
]h(r)r2dr
I(xi < C) exp[−{xi−µ
(t)}22(σ(t))2
]+∫ xi/C
0 exp[−{(xi/ω)−µ(t)}2
2(σ(t))2
]h(ω)ω dω
≡ xiψ3(θ(t), xi).
Hence we can write
Q(θ|θ(t)) = −n2
ln(σ2)− nµ2
2σ2− 1
2σ2
n∑i=1
{(xi)
2 − 2µxi}ψ1(θ(t), xi)
− 1
2σ2
n∑i=1
(x2iψ2(θ(t), xi)− 2µxiψ3(θ(t), xi).
M-step. By maximizing Q(θ|θ(t)) with respect to θ, we obtain the following equations which definethe sequence of EM iterations:
µ(t+1) =1
n
n∑i=1
[xi(ψ1(θ(t), xi) + ψ3(θ(t), xi))
],
(σ(t+1))2 =1
n
n∑i=1
[x2i (ψ1(θ(t), xi) + ψ2(θ(t), xi))
]− (µ(t+1))2
50
where the expressions for ψ1(θ(t), xi), ψ1(θ(t), xi) and ψ1(θ(t), xi) are given above.To compute the observed Fisher information in this case, we can express the pdf of a single
observation x as
kθ(x) =1
σφ(x− µσ
)I(x < C) +
∫ xC
0φ
( xr − µσ
)I(x > 0)
h(r)
rdr, (57)
where φ(.) is the standard normal pdf . This yields
∂kθ(x)
∂µ=x− µσ3
φ
(x− µσ
)I(x < C) +
∫ xC
0
xr − µσ3
φ
( xr − µσ
)I(x > 0)
h(r)
rdr, (58)
and hence
∂2kθ(x)
∂µ2= −kθ(x)
σ2+
(x− µ)2
σ4
1
σφ
(x− µσ
)I(x < C)
+
∫ xC
0
(xr − µ)2
σ4
1
σφ
( xr − µσ
)I(x > 0)
h(r)
rdr. (59)
We also have
∂2kθ(x)
∂µ∂σ2= −3(x− µ)
2σ5φ
(x− µσ
)I(x < C)
− 3
2σ5
∫ xC
0(x
r− µ)φ
( xr − µσ
)I(x > 0)
h(r)
rdr
+x− µσ3
[− 1
2σ2+
(x− µ)2
2σ4]φ
(x− µσ
)I(x < C)
+
∫ xC
0
xr − µσ3
[− 1
2σ2+
(xr − µ)2
2σ4
]φ
( xr − µσ
)I(x > 0)
h(r)
rdr. (60)
Lastly, we can write
∂kθ(x)
∂σ2= − 1
2σ2kθ(x) +
1
σφ
(x− µσ
)[− 1
2σ2+
(x− µ)2
2σ4
]I(x < C)
+
∫ xC
0φ
( xr − µσ
)I(x > 0)
[− 1
2σ2+
(xr − µ)2
2σ4
]h(r)
rdr, (61)
so that
∂2kθ(x)
∂(σ2)2=
1
2σ4kθ(x)− 1
2σ2
∂kθ(x)
∂σ2+ φ
(x− µσ
)[3
4σ5− 5(x− µ)2
4σ7
]I(x < C)
+
∫ xC
0φ
( xr − µσ
)I(x > 0)
[3
4σ5−
5(xr − µ)2
4σ7
]h(r)
rdr
+1
σφ
(x− µσ
)[− 1
2σ2+
(x− µ)2
2σ4
]2
I(x < C)
+
∫ xC
0φ
( xr − µσ
)I(x > 0)
[− 1
2σ2+
(xr − µ)2
2σ4
]2h(r)
rdr. (62)
51
We can use the above expressions to compute the elements of the observed Fisher informationmatrix.
C3. Lognormal distribution
We now assume that Y ∼ fθ(y) = 1
y√
2πσ2exp
[− (ln y−µ)2
2σ2
], 0 < y <∞, where θ = (µ, σ2). Then
the complete data likelihood function is
L(θ|vc) =
n∏i=1
{1
xi√
2πσ2exp
[−(lnxi − µ)2
2σ2
]}∆i{
ri
xi√
2πσ2exp
[−(ln(xi/ri)− µ)2
2σ2
]}1−∆i
∝n∏i=1
{1√σ2
exp
[−(lnxi − µ)2
2σ2
]}∆i{
1√σ2
exp
[−(ln(xi/ri)− µ)2
2σ2
]}1−∆i
= (σ2)−n/2n∏i=1
{exp
[−(lnxi − µ)2
2σ2
]}∆i{
exp
[−(ln(xi/ri)− µ)2
2σ2
]}1−∆i
,
and we get the complete data log-likelihood function as
`(θ|vc) = −n2
ln(σ2)− 1
2σ2
n∑i=1
{∆i(lnxi − µ)2 + (1−∆i)(ln
xiri− µ)2
}
= −n2
ln(σ2)− nµ2
2σ2− 1
2σ2
n∑i=1
{∆i[(lnxi)
2 − 2µ lnxi] + (1−∆i)[(lnxiri
)2 − 2µ lnxiri
]
}.
Case (i). The EM algorithm for computing the MLE of θ based on (x1,∆1), . . . , (xn,∆n) is asfollows.
E-step.
Q(θ|θ(t)) = Eθ(t) [`(θ|vc)|vi,obs]
= −n2
ln(σ2)− nµ2
2σ2− 1
2σ2
n∑i=1
{∆i[(lnxi)
2 − 2µ lnxi]}
− 1
2σ2
n∑i=1
{(1−∆i)
(Eθ(t) [(ln
xiri
)2|xi,∆i = 0]− 2µEθ(t) [(lnxiri
)|xi,∆i = 0]
)}where
Eθ(t) [(lnxiri
)2|xi,∆i = 0] =
∫ xi/C0 (ln xi
r )2 exp[−{ln(xi/r)−µ(t)}2
2(σ(t))2
]h(r)dr∫ xi/C
0 exp[−{ln(xi/ω)−µ(t)}2
2(σ(t))2
]h(ω)dω
,
Eθ(t) [(lnxiri
)|xi,∆i = 0] =
∫ xi/C0 (ln xi
r ) exp[−{ln(xi/r)−µ(t)}2
2(σ(t))2
]h(r)dr∫ xi/C
0 exp[−{ln(xi/ω)−µ(t)}2
2(σ(t))2
]h(ω)dω
.
M-step. By maximizing Q(θ|θ(t)) with respect to θ, we obtain the following equations which define
52
the sequence of EM iterations:
µ(t+1) =1
n
n∑i=1
{∆i lnxi + (1−∆i)Eθ(t) [(ln
xiri
)|xi,∆i = 0]
},
(σ(t+1))2 =1
n
(n∑i=1
{∆i(lnxi)
2 + (1−∆i)Eθ(t) [(lnxiri
)2|xi,∆i = 0]
}− n(µ(t+1))2
),
where the expressions for Eθ(t) [(lnxiri
)2|xi,∆i = 0] and Eθ(t) [(lnxiri
)|xi,∆i = 0] are given above.To compute the observed Fisher information in this case, recalling Result 2 given in Appendix
A of the paper, a direct computation using the above formulas shows that for a generic term withx and ∆,
∂l(θ)
∂µ=
(lnx− µ)∆
σ2+ (1−∆)
∫ xC
0 e−(ln x−ln r−µ)2
2σ2(lnx−ln r−µ)2
σ2 h(r)dr∫ xC
0 e−(ln x−ln r−µ)2
2σ2 h(r)dr
(63)
leading to
∂2l(θ)
∂µ2= − 1
σ2+ (1−∆)[
∫ xC
0 e−(ln x−ln r−µ)2
2σ2 ( (lnx−ln r−µ)2
σ2 )2h(r)dr∫ xC
0 e−(ln x−ln r−µ)2
2σ2 h(r)dr
−{∫ xC
0 e−(ln x−ln r−µ)2
2σ2(lnx−ln r−µ)2
σ2 h(r)dr∫ xC
0 e−(ln x−ln r−µ)2
2σ2 h(r)dr
}2]. (64)
Likewise,
∂2l(θ)
∂µ∂σ2= −(lnx− µ)∆
σ4+ (1−∆)[−
∫ xC
0 e−(ln x−ln r−µ)2
2σ2 ( (lnx−ln r−µ)2
σ4 )h(r)dr∫ xC
0 e−(ln x−ln r−µ)2
2σ2 h(r)dr
+1
2σ6
∫ xC
0 e−(ln x−ln r−µ)2
2σ2 (lnx− ln r − µ)3h(r)dr∫ xC
0 e−(ln x−ln r−µ)2
2σ2 h(r)dr
− 1
2σ6
∫ xC
0 e−(ln x−ln r−µ)2
2σ2 (lnx− ln r − µ)h(r)dr∫ xC
0 e−(ln x−ln r−µ)2
2σ2 (lnx− ln r − µ)2h(r)dr∫ xC
0 e−(ln x−ln r−µ)2
2σ2 h(r)dr2
].(65)
53
Finally,
∂2l(θ)
(∂σ2)2=
1
2σ4− (lnx− µ)2∆
σ6+ (1−∆)[− 1
σ6
∫ xC
0 e−(ln x−ln r−µ)2
2σ2 (lnx− ln r − µ)2h(r)dr∫ xC
0 e−(ln x−ln r−µ)2
2σ2 h(r)dr
+1
4σ8
1
2σ6
∫ xC
0 e−(ln x−ln r−µ)2
2σ2 (lnx− ln r − µ)4h(r)dr∫ xC
0 e−(ln x−ln r−µ)2
2σ2 h(r)dr
− 1
4σ8{∫ xC
0 e−(ln x−ln r−µ)2
2σ2 (lnx− ln r − µ)2h(r)dr∫ xC
0 e−(ln x−ln r−µ)2
2σ2 h(r)dr
}2]. (66)
Case (ii). The EM algorithm for computing the MLE of θ based on (x1, . . . , xn) is as follows.
E-step.
Q(θ|θ(t)) = Eθ(t) [`(θ|vc)|vii,obs]
= −n2
ln(σ2)− nµ2
2σ2− 1
2σ2
n∑i=1
{{(lnxi)2 − 2µ lnxi}Eθ(t) [∆i|xi]
}− 1
2σ2
n∑i=1
{Eθ(t) [(1−∆i)(ln
xiri
)2|xi]− 2µEθ(t) [(1−∆i)(lnxiri
)|xi]}
where
Eθ(t) [∆i|xi] =I(xi < C) exp
[− (lnxi−µ(t))2
2(σ(t))2
]I(xi < C) exp
[− (lnxi−µ(t))2
2(σ(t))2
]+∫ xi/C
0 exp[− (ln(xi/ω)−µ(t))2
2(σ(t))2
]h(ω)dω
.
Eθ(t) [(1−∆i)(lnxiri
)2|xi]
=
∫ xi/C0 (ln xi
r )2 exp[−{ln(xi/r)−µ(t)}2
2(σ(t))2
]h(r)dr
I(xi < C) exp[−{lnxi−µ
(t)}22(σ(t))2
]+∫ xi/C
0 exp[−{ln(xi/ω)−µ(t)}2
2(σ(t))2
]h(ω)dω
,
Eθ(t) [(1−∆i)(lnxiri
)|xi] =
∫ xi/C0 (ln xi
r ) exp[−{ln(xi/r)−µ(t)}2
2(σ(t))2
]h(r)dr
I(xi < C) exp[−{lnxi−µ
(t)}22(σ(t))2
]+∫ xi/C
0 exp[−{ln(xi/ω)−µ(t)}2
2(σ(t))2
]h(ω)dω
.
M-step. By maximizing Q(θ|θ(t)) with respect to θ, we obtain the following equations which definethe sequence of EM iterations:
µ(t+1) =1
n
n∑i=1
{(lnxi)Eθ(t) [∆i|xi] + Eθ(t) [(1−∆i)(ln
xiri
)|xi]},
(σ(t+1))2 =1
n
(n∑i=1
{(lnxi)
2Eθ(t) [∆i|xi] + Eθ(t) [(1−∆i)(lnxiri
)2|xi]}− n(µ(t+1))2
),
54
where formulas for Eθ(t) [∆i|xi], Eθ(t) [(1 − ∆i)(lnxiri
)2|xi], and Eθ(t) [(1 − ∆i)(lnxiri
)|xi] are givenabove.
To compute the observed Fisher information in this case, note that (by Result 3 of AppendixA of the paper) the loglikelihood based on a generic x is given by ln k(x, θ) where
k(x, θ) ∼ 1
σ[e−
(ln x−µ)2
2σ2 I(x < C) +
∫ xC
0e−
(ln x−ln r−µ)2
2σ2 I(x > 0)h(r)dr]. (67)
Hence we get
∂ ln k(x, θ)
∂µ=e−
(ln x−µ)2
2σ2lnx−µσ2 I(x < C) +
∫ xC
0 e−(ln x−ln r−µ)2
2σ2 I(x > 0) lnx−ln r−µσ2 h(r)dr
e−(ln x−µ)2
2σ2 I(x < C) +∫ xC
0 e−(ln x−ln r−µ)2
2σ2 I(x > 0)h(r)dr
= − µ
σ2+
1
σ2
e− (ln x−µ)2
2σ2 (lnx)I(x < C) +∫ xC
0 e−(ln x−ln r−µ)2
2σ2 I(x > 0)(lnx− ln r)h(r)dr
e−(ln x−µ)2
2σ2 I(x < C) +∫ xC
0 e−(ln x−ln r−µ)2
2σ2 I(x > 0)h(r)dr
(68)
This readily yields
∂2 ln k(x, θ)
∂µ2= − 1
σ2
+1
σ4
e− (ln x−µ)2
2σ2 (lnx)(lnx− µ)I(x < C) +∫ xC
0e−
(ln(x/r)−µ)2
2σ2 I(x > 0) ln(x/r)(ln(x/r)− µ)h(r)dr
e−(ln x−µ)2
2σ2 I(x < C) +∫ xC
0e−
(ln x−ln r−µ)22σ2 I(x > 0)h(r)dr
− 1
σ4
{[e−
(ln x−µ)2
2σ2 (lnx)I(x < C) +
∫ xC
0
e−(ln(x/r)−µ)2
2σ2 I(x > 0) ln(x/r)h(r)dr
]
×
[e−
(ln x−µ)2
2σ2 (lnx− µ)I(x < C) +
∫ xC
0
e−(ln(x/r)−µ)2
2σ2 I(x > 0)(ln(x/r)− µ)h(r)dr
]
×
[e−
(ln x−µ)2
2σ2 I(x < C) +
∫ xC
0
e−(ln(x/r)−µ)2
2σ2 I(x > 0)h(r)dr
]−2 . (69)
From (68), we get
∂2 ln k(x, θ)
∂µ∂σ2=
µ
σ4− 1
σ4
e− (ln x−µ)2
2σ2 (lnx)I(x < C) +∫ xC
0e−
(ln(x/r)−µ)2
2σ2 I(x > 0) ln(x/r)h(r)dr
e−(ln x−µ)2
2σ2 I(x < C) +∫ xC
0e−
(ln(x/r)−µ)22σ2 I(x > 0)h(r)dr
+
1
2σ6
e− (ln x−µ)2
2σ2 (lnx)(lnx− µ)2I(x < C) +∫ xC
0e−
(ln(x/r)−µ)2
2σ2 I(x > 0) ln(x/r)(ln(x/r)− µ)2h(r)dr
e−(ln x−µ)2
2σ2 I(x < C) +∫ xC
0e−
(ln(x/r)−µ)22σ2 I(x > 0)h(r)dr
− 1
2σ6
{[e−
(ln x−µ)2
2σ2 (lnx)I(x < C) +
∫ xC
0
e−(ln(x/r)−µ)2
2σ2 I(x > 0) ln(x/r)h(r)dr
]
×
[e−
(ln x−µ)2
2σ2 (lnx− µ)2I(x < C) +
∫ xC
0
e−(ln(x/r)−µ)2
2σ2 I(x > 0)(ln(x/r)− µ)2h(r)dr
]
×
[e−
(ln x−µ)2
2σ2 I(x < C) +
∫ xC
0
e−(ln(x/r)−µ)2
2σ2 I(x > 0)h(r)dr
]−2 . (70)
55
On the other hand, we get
∂ ln k(x, θ)
∂σ2= − 1
2σ2
+1
2σ4
e− (ln x−µ)2
2σ2 (lnx− µ)2I(x < C) +∫ xC
0 e−(ln x−ln r−µ)2
2σ2 I(x > 0)(lnx− ln r − µ)2h(r)dr
e−(ln x−µ)2
2σ2 I(x < C) +∫ xC
0 e−(ln x−ln r−µ)2
2σ2 I(x > 0)h(r)dr
,and hence,
∂2 ln k(x, θ)
∂(σ2)2=
1
2σ4
− 1
σ6
e− (ln x−µ)2
2σ2 (lnx− µ)2I(x < C) +∫ xC
0 e−(ln x−ln r−µ)2
2σ2 I(x > 0)(lnx− ln r − µ)2h(r)dr
e−(ln x−µ)2
2σ2 I(x < C) +∫ xC
0 e−(ln x−ln r−µ)2
2σ2 I(x > 0)h(r)dr
+
1
4σ8
e− (ln x−µ)2
2σ2 (lnx− µ)4I(x < C) +∫ xC
0 e−(ln x−ln r−µ)2
2σ2 I(x > 0)(lnx− ln r − µ)4h(r)dr
e−(ln x−µ)2
2σ2 I(x < C) +∫ xC
0 e−(ln x−ln r−µ)2
2σ2 I(x > 0)h(r)dr
− 1
4σ8
e− (ln x−µ)2
2σ2 (lnx− µ)2I(x < C) +∫ xC
0 e−(ln x−ln r−µ)2
2σ2 I(x > 0)(lnx− ln r − µ)2h(r)dr
e−(ln x−µ)2
2σ2 I(x < C) +∫ xC
0 e−(ln x−ln r−µ)2
2σ2 I(x > 0)h(r)dr
2
.
56
APPENDIX D: MLEs AND FISHER INFORMATION UNDER TOP CODING
In this Appendix, we present the MLEs, along with the expressions for the observed Fisherinformation matrix for the three parametric models: exponential, normal and lognormal.
D1. Exponential distributionAssume y1, . . . , yn is a random sample from the exponential distribution fθ(y) = 1
θe−y/θ, y > 0.
Let xi = min{yi, C}, and ∆i = I(yi ≤ C), for i = 1, . . . , n. The likelihood for θ based on theobserved data wobs = (x1, . . . , xn,∆1, . . . ,∆n) is given by
L(θ|wobs) = (1
θ)∑ni=1 ∆i × e−
∑ni=1 xiθ .
It is easily seen that the MLE of θ is
θMLE =
∑ni=1 xi∑ni=1 ∆i
,
and the observed Fisher information is
(∑n
i=1 ∆i)2∑n
i=1 xi.
D2. Normal distributionLet C denote the known top code threshold. Assume y1, . . . , yn ∼ iid N(µ, σ2) and let xi =
min{yi, C} and ∆i = I(yi ≤ C), i = 1, . . . , n. In this case we can denote the complete and observeddata, respectively, as
wc = (y1, . . . , yn), wobs = (x1, . . . , xn,∆1, . . . ,∆n).
Obviously the complete data loglikelihood is given by
`(µ, σ2|wc) ∼ −n
2ln(σ2)− 1
2σ2
n∑i=1
y2i +
µ
σ2
n∑i=1
yi −nµ2
2σ2. (71)
The MLE of (µ, σ2) based on the observed data wobs can be computed via the EM algorithm. TheE and M steps are as follows.E-step. We have
Q(θ|θ(t)) = Eθ(t) [`(µ, σ2|wc)|wobs]
= −n2
ln(σ2)− 1
2σ2
n∑i=1
Eθ(t) [y2i |wobs] +
µ
σ2
n∑i=1
Eθ(t) [yi|wobs]−nµ2
2σ2
= −n2
ln(σ2)− 1
2σ2
n∑i=1
Eθ(t) [y2i |xi,∆i] +
µ
σ2
n∑i=1
Eθ(t) [yi|xi,∆i]−nµ2
2σ2. (72)
57
where
Eθ(t) [yi|xi,∆i] = xi∆i + (1−∆i)
∫∞C
yσ(t)φ
(y−µ(t)σ(t)
)dy
1− Φ(C−µ(t)σ(t)
) , (73)
Eθ(t) [y2i |xi,∆i] = x2
i∆i + (1−∆i)
∫∞C
y2
σ(t)φ(y−µ(t)σ(t)
)dy
1− Φ(C−µ(t)σ(t)
) . (74)
It is easy to verify by direct computation that
ψ1(θ) ≡∫∞C
yσφ(y−µ
σ
)dy
1− Φ(C−µσ
) = µ+ σφ(C−µσ
)1− Φ
(C−µσ
) (75)
ψ2(θ) ≡∫∞C
y2
σ φ(y−µ
σ
)dy
1− Φ(C−µσ
) = µ2 + σ2 + σ(µ+ C)φ(C−µσ
)1− Φ
(C−µσ
) . (76)
We can therefore simplify Q(θ|θ(t)) as
Q(θ|θ(t)) = −n2
ln(σ2)− 1
2σ2
n∑i=1
x2i∆i −
1
2σ2ψ2(θ(t))
n∑i=1
(1−∆i) (77)
+µ
σ2
n∑i=1
xi∆i +µ
σ2ψ1(θ(t))
n∑i=1
(1−∆i)−nµ2
2σ2.
M-step. Using (77) we can simplify ∂Q(θ|θ(t)∂µ = 0 and ∂Q(θ|θ(t))
∂σ2 = 0, resulting in the solution
µ =1
n[
n∑i=1
xi∆i + ψ1(θ(t))
n∑i=1
(1−∆i)],
σ2 =1
n[
n∑i=1
x2i∆i + ψ2(θ)
n∑i=1
(1−∆i)]− µ2. (78)
Thus the EM algorithm in this case is defined by the following iterations:
µ(t+1) =1
n[
n∑i=1
xi∆i + ψ1(θ(t))n∑i=1
(1−∆i)],
(σ(t+1))2 =1
n[n∑i=1
x2i∆i + ψ2(θ(t))
n∑i=1
(1−∆i)]− [µ(t+1)]2. (79)
We now discuss the computation of observed Fisher information. Since the likelihood functionfor θ based on wobs is given by
L(θ|wobs) ∼n∏i=1
([1
σφ
(xi − µσ
)]∆i[Φ
(xi − µσ
)]1−∆i),
58
the loglikelihood `(θ) is obtained as
`(θ|wobs) ∼ − ln(σ)
(n∑i=1
∆i
)+
n∑i=1
∆i lnφ
(xi − µσ
)+
n∑i=1
(1−∆i) ln Φ
(xi − µσ
). (80)
In order to derive the elements of the Fisher information matrix, we shall use the following prop-erties: φ′(u) = −uφ(u) and
∂
∂σ2
[φ(xi−µ
σ
)Φ(xi−µσ )
]=
1
2σ2
φ(xi−µ
σ
) (xi−µσ
)Φ(xi−µ
σ
) [(xi − µσ
)−φ(xi−µ
σ
)Φ(xi−µ
σ
)] ,where φ(u) is the standard normal pdf , and Φ(u) = 1 − Φ(u), where Φ(u) is the standard normalcdf . By straightforward algebra, we get
∂`(θ|wobs)
∂µ= − 1
σ
n∑i=1
∆iφ′(xi−µ
σ
)φ(xi−µσ )
+1
σ
n∑i=1
(1−∆i)φ(xi−µ
σ
)Φ(xi−µ
σ
)=
1
σ2
n∑i=1
∆i(xi − µ) +1
σ
n∑i=1
(1−∆i)φ(xi−µ
σ
)Φ(xi−µ
σ
) ,∂`(θ|wobs)
∂σ2= − 1
2σ2
n∑i=1
∆i +1
2σ4
n∑i=1
∆i(xi − µ)2 +1
2σ3
n∑i=1
(1−∆i)(xi − µ)φ(xi−µ
σ
)Φ(xi−µ
σ
) , (81)
and hence,
∂2`(θ|wobs)
∂µ2= − 1
σ2
n∑i=1
∆i +1
σ2
n∑i=1
(1−∆i)
(xi − µσ
)φ(xi−µ
σ
)Φ(xi−µ
σ
) − 1
σ2
n∑i=1
(1−∆i)
[φ(xi−µ
σ
)Φ(xi−µ
σ
)]2
,
∂2`(θ|wobs)
∂µ∂σ2= − 1
σ4
n∑i=1
∆i(xi − µ)− 1
2σ3
n∑i=1
(1−∆i)φ(xi−µ
σ
)Φ(xi−µ
σ
) +1
σ
n∑i=1
(1−∆i)∂
σ2
[φ(xi−µ
σ
)Φ(xi−µ
σ
)] ,∂2`(θ|wobs)
∂(σ2)2=
1
2σ4
n∑i=1
∆i −1
σ6
n∑i=1
∆i(xi − µ)2 − 3
4σ5
n∑i=1
(1−∆i)(xi − µ)φ
(xi−µσ
)Φ(xi−µ
σ
)+
1
4σ4
n∑i=1
(1−∆i)u3i
[φ(xi−µ
σ
)Φ(xi−µ
σ
)]− 1
4σ4
n∑i=1
(1−∆i)u2i
[φ(xi−µ
σ
)Φ(xi−µ
σ
)]2
. (82)
D3. Lognormal distributionWe once again use the property that if y1, . . . , yn is a random sample from a lognormal distri-
bution, then ln y1, . . ., ln yn is a sample from a normal distribution. We can now apply the normaltheory results given in the previous section upon replacing yi by ln yi and C by lnC.
59
APPENDIX E: SIMULATION RESULTS
In this Appendix, we present extensive numerical results for comparing multiple imputationand noise multiplication for the exponential, normal and lognormal models. We consider the caseof fully masked samples (where all values are replaced with multiply imputed or noise multiplieddata), as well as partially masked samples (where the top coded data are replaced with multiplyimputed or noise multiplied data).
The notations used in the tables are as given in Section 6 of the paper. The notation CD denotesthe case of complete data without any masking. MI denotes multiple imputation used to generatefully masked data. MI.C and MI.D are used to denote parametric multiple imputation based on thecomplete data, and based on the deleted data, respectively. These are explained in Section 4.2. Inthe case of a top coded sample with a top coding threshold C, values beyond a threshold CI werealso replaced with imputed values, where CI < C, following An and Little (2007). Two choices weremade for CI following the recipe prescribed by An and Little (2007). If nS denotes the number ofvalues beyond the top coding threshold C, the two choices of CI correspond to thresholds for which2nS values in the sample are larger, and 4nS values are larger. Since these values approximatelycorrespond to the 90th and 80th percentiles of the distribution when C is the 95th percentile, theseare denoted (following An and Little, 2007) by MI.C90 and MI.C80, respectively, in the case ofmultiple imputation based on the complete data, and denoted by MI.D90 and MI.D80, respectively,in the case of multiple imputation based on the deleted data. Throughout we have used 50 sets ofimputed values under MI.
The notations used under noise multiplication are as follows. We have used either a Uniform(1−ε, 1 + ε) distribution or a customized prior distribution for the noise multiplication. In the case ofUniform(1 − ε, 1 + ε), the notation NM10U denotes noise multiplication with the above uniformdistribution under the choice ε = 0.10. NM20U, NM30U etc. are similarly defined. Furthermore,NM10C, NM20C etc. are the corresponding notations under the customized prior whose mean andvariance match those of the respective uniform distributions. Additional notation used under theuniform noise distribution Uniform(1 − ε, 1 + ε) is as follows. For the choice ε = 0.1, NM10.1 andNM10.2 represent the case of observing the (xi,∆i)s, or only the xis; these are Case (i) and Case(ii) explained in Section 3 for the three different distributions. NM20.1, NM20.2 etc. are similarlydefined. In addition to the above notations, entries in the tables corresponding to CENS denoteresults from the analysis of the censored data, i.e., the top coded data.
Table E1 − Table E36 are for comparing fully masked samples where all values have beenprotected, and are as follows:
Table E1 − Table E3: Exponential distribution
Table E4 − Table E21: Lognormal distribution
Table E22 − Table E36: Normal distribution
Table E37 − Table E84 are for comparing partially masked samples where the extreme valueshave been protected, and are as follows:
Table E37 − Table E40: Exponential distribution
Table E41 − Table E64: Lognormal distribution
Table E65 − Table E84: Normal distribution
60
Tab
leE
1:In
fere
nce
for
the
mea
nb
ased
onfu
lly
mas
ked
Exp
onen
tial
(mea
n=
1)d
ata
Res
ult
sfo
rn
=30
Res
ult
sfo
rn
=50
RM
SE
Bia
sS
DS
DC
vg.
Rel
.R
MS
EB
ias
SD
SD
Cvg.
Rel
.×
103×
103
×10
3×
103
%L
en.
×10
3×
103
×10
3×
103
%L
en.
CD
183.7
4-3
.17
183.
7318
1.99
93.1
81.
000
140.
09-0
.43
140.
1014
1.36
94.2
81.
000
MI
211.8
568
.36
200.
5420
5.74
96.0
81.
130
154.
3440
.56
148.
9315
3.12
96.1
01.
083
NM
10U
184.2
9-3
.23
184.
2818
2.57
93.1
41.
003
140.
65-0
.12
140.
6714
1.86
94.3
41.
004
NM
10C
184.1
4-2
.91
184.
1418
2.63
92.9
81.
003
140.
78-0
.24
140.
7914
1.85
94.2
01.
003
NM
20U
186.0
7-2
.85
186.
0618
4.36
93.0
21.
013
141.
580.
1414
1.60
143.
2593
.98
1.01
3N
M20C
186.2
4-2
.12
186.
2518
4.46
92.9
81.
014
141.
620.
0314
1.64
143.
2294
.18
1.01
3N
M30U
191.1
7-0
.31
191.
1918
7.62
92.9
61.
031
144.
860.
4614
4.88
145.
4794
.42
1.02
9N
M30C
188.9
6-0
.80
188.
9718
7.37
93.0
81.
030
144.
410.
6214
4.42
145.
4094
.14
1.02
9N
M40U
193.5
50.
4019
3.57
191.
5193
.02
1.05
214
7.19
1.28
147.
2014
8.49
94.1
01.
050
NU
40C
193.0
10.
2319
3.03
190.
9892
.84
1.04
914
7.03
0.40
147.
0414
8.06
94.3
81.
047
NM
50U
198.2
8-0
.96
198.
3019
5.90
92.7
21.
076
152.
380.
5915
2.40
151.
9794
.22
1.07
5N
M50C
199.1
11.
1819
9.13
195.
1092
.94
1.07
215
0.62
2.77
150.
6115
1.49
94.1
41.
072
NM
60U
202.4
0-0
.74
202.
4220
1.48
92.6
01.
107
155.
622.
5415
5.61
156.
5194
.40
1.10
7N
M60C
201.0
22.
9220
1.02
199.
7092
.94
1.09
715
5.03
4.03
154.
9915
5.00
93.9
41.
096
NM
70U
210.8
04.
6521
0.77
209.
0192
.80
1.14
816
1.33
4.94
161.
2716
1.82
94.6
01.
145
NM
70C
205.9
13.
2120
5.90
204.
0493
.18
1.12
115
7.70
3.59
157.
6815
8.30
93.9
41.
120
NM
80U
216.0
4-0
.50
216.
0621
5.32
92.8
81.
183
164.
931.
9316
4.94
166.
9994
.30
1.18
1N
M80C
211.1
07.
1821
1.00
209.
1093
.14
1.14
916
0.19
4.91
160.
1316
1.82
94.2
01.
145
NM
90U
222.7
92.
1722
2.80
224.
5493
.04
1.23
417
2.99
4.65
172.
9417
4.13
94.4
81.
232
NM
90C
215.4
09.
4921
5.22
213.
7793
.34
1.17
516
6.88
5.43
166.
8116
5.08
93.7
41.
168
61
Tab
leE
2:In
fere
nce
for
the
mea
nb
ased
onfu
lly
mas
ked
Exp
onen
tial
(mea
n=
1)d
ata
Res
ult
sfo
rn
=10
0R
esu
lts
forn
=20
0
RM
SE
Bia
sS
DS
DC
vg.
Rel
.R
MS
EB
ias
SD
SD
Cvg.
Rel
.×
103
×10
3×
103
×10
3%
Len
.×
103×
103×
103×
103
%L
en.
CD
100.
44-1
.62
100.
4499
.84
94.1
61.
000
71.3
90.
4171
.40
70.7
494
.22
1.00
0M
I106.
4418
.91
104.
7510
4.94
95.3
41.
051
74.3
210
.71
73.5
573
.24
95.0
01.
035
NM
10U
100.
67-1
.78
100.
6610
0.15
94.3
41.
003
71.6
00.
3971
.61
70.9
794
.02
1.00
3N
M10
C100.
93-1
.47
100.
9310
0.18
94.2
61.
003
71.6
60.
3671
.66
70.9
794
.38
1.00
3N
M20
U101.
54-1
.31
101.
5410
1.15
94.3
21.
013
72.2
30.
4572
.24
71.6
694
.64
1.01
3N
M20
C101.
68-1
.17
101.
6910
1.16
94.5
61.
013
72.1
80.
6072
.19
71.6
694
.40
1.01
3N
M30
U103.
20-1
.55
103.
2010
2.66
94.7
81.
028
73.0
40.
4573
.05
72.7
494
.66
1.02
8N
M30
C103.
41-0
.76
103.
4210
2.69
94.5
21.
029
72.9
80.
5972
.99
72.7
294
.50
1.02
8N
M40
U106.
26-0
.71
106.
2710
4.79
94.2
81.
050
75.0
00.
9375
.00
74.2
394
.66
1.04
9N
U40C
104.
83-0
.43
104.
8410
4.62
94.3
61.
048
74.6
00.
4574
.61
74.0
694
.54
1.04
7N
M50
U108.
85-1
.29
108.
8510
7.26
94.2
41.
074
75.6
70.
5475
.67
75.9
894
.76
1.07
4N
M50
C107.
64-0
.68
107.
6510
6.78
93.8
81.
070
76.1
71.
3876
.17
75.6
894
.56
1.07
0N
M60
U111.
01-0
.02
111.
0211
0.38
94.4
21.
106
78.3
91.
1378
.39
78.1
394
.70
1.10
4N
M60
C108.
43-0
.35
108.
4410
9.15
94.2
61.
093
77.8
41.
8377
.83
77.3
994
.68
1.09
4N
M70
U114.
37-0
.62
114.
3811
3.76
94.0
81.
139
81.2
21.
3681
.21
80.5
894
.58
1.13
9N
M70
C110.
821.
0911
0.83
111.
6994
.90
1.11
980
.03
1.64
80.0
279
.05
94.4
81.
118
NM
80U
118.
160.
1211
8.17
117.
8494
.26
1.18
082
.96
1.43
82.9
683
.40
94.8
21.
179
NM
80C
113.
601.
3911
3.60
114.
0894
.76
1.14
381
.89
1.78
81.8
880
.72
94.0
41.
141
NM
90U
124.
63-0
.08
124.
6412
2.47
94.1
41.
227
87.0
52.
2087
.03
86.7
694
.76
1.22
6N
M90
C117.
321.
8711
7.32
116.
3594
.46
1.16
583
.89
1.90
83.8
882
.31
94.6
01.
164
62
Tab
leE
3:In
fere
nce
for
the
mea
nb
ased
onfu
lly
mas
ked
Exp
onen
tial
(mea
n=
1)d
ata
Res
ult
sfo
rn
=10
00R
esu
lts
forn
=20
00
RM
SE
Bia
sS
DS
DC
vg.
Rel
.R
MS
EB
ias
SD
SD
Cvg.
Rel
.×
103
×10
3×
103×
103
%L
en.
×10
3×
103×
103×
103
%L
en.
CD
31.0
5-1
.13
31.0
331
.59
95.1
21.
000
22.6
1-0
.15
22.6
122
.36
94.7
61.
000
MI
31.6
90.
7831
.69
32.3
195
.50
1.02
323
.12
0.93
23.1
022
.84
94.9
21.
021
NM
10U
31.1
5-1
.08
31.1
331
.69
95.0
61.
003
22.6
9-0
.17
22.6
922
.43
94.6
81.
003
NM
10C
31.1
7-1
.14
31.1
531
.69
95.1
41.
003
22.7
5-0
.15
22.7
522
.43
94.7
41.
003
NM
20U
31.4
0-1
.16
31.3
931
.99
95.2
41.
013
22.8
9-0
.06
22.8
922
.65
94.8
61.
013
NM
20C
31.4
0-0
.98
31.3
932
.00
95.0
81.
013
22.8
4-0
.15
22.8
422
.65
94.8
21.
013
NM
30U
31.9
1-1
.21
31.8
932
.48
95.2
21.
028
23.2
8-0
.28
23.2
822
.99
94.5
41.
028
NM
30C
32.0
3-0
.97
32.0
232
.47
95.2
21.
028
23.1
8-0
.16
23.1
822
.98
94.6
61.
028
NM
40U
32.8
1-1
.09
32.7
933
.13
94.8
61.
049
23.6
5-0
.09
23.6
623
.45
94.9
01.
049
NU
40C
32.6
0-1
.19
32.5
833
.07
95.4
81.
047
23.6
1-0
.10
23.6
123
.41
94.7
41.
047
NM
50U
33.3
4-1
.18
33.3
233
.92
95.3
61.
074
24.2
7-0
.41
24.2
724
.00
94.7
41.
074
NM
50C
32.8
2-1
.20
32.8
033
.76
95.2
61.
069
24.1
7-0
.06
24.1
723
.90
94.6
21.
069
NM
60U
34.5
8-0
.85
34.5
734
.87
94.9
81.
104
24.7
8-0
.05
24.7
824
.67
94.5
41.
104
NM
60C
34.1
0-0
.82
34.1
034
.52
95.1
81.
093
24.6
6-0
.28
24.6
624
.42
94.5
21.
092
NM
70U
35.8
7-1
.04
35.8
635
.95
95.0
21.
138
25.5
5-0
.24
25.5
525
.44
94.7
61.
138
NM
70C
34.4
3-1
.38
34.4
035
.25
95.2
61.
116
24.9
5-0
.26
24.9
524
.96
95.1
21.
116
NM
80U
36.8
1-0
.70
36.8
137
.21
95.1
21.
178
26.3
2-0
.21
26.3
326
.33
95.0
01.
178
NM
80C
35.6
1-0
.93
35.6
036
.01
94.8
81.
140
25.8
40.
1125
.84
25.4
994
.66
1.14
0N
M90U
38.0
3-1
.59
38.0
038
.65
95.2
21.
223
27.5
90.
0727
.59
27.3
794
.78
1.22
4N
M90C
36.4
1-1
.21
36.3
936
.71
95.4
81.
162
26.2
30.
1726
.23
25.9
994
.60
1.16
3
63
Tab
leE
4:In
fere
nce
for
the
log
scal
em
eanµ
bas
edfu
lly
mas
kedLN
(µ=
0,σ
2=
1)d
ata
Res
ult
sfo
rn
=30
Res
ult
sfo
rn
=50
RM
SE
Bia
sS
DS
DC
vg.
Rel
.R
MS
EB
ias
SD
SD
Cvg.
Rel
.×
103×
103
×10
3×
103
%L
en.
×10
3×
103
×10
3×
103
%L
en.
CD
180.0
8-0
.10
180.
0917
8.24
94.3
61.
000
142.
920.
9514
2.93
139.
2994
.06
1.00
0M
I18
4.6
5-0
.71
184.
6718
8.34
94.9
21.
057
145.
791.
1914
5.80
145.
0494
.64
1.04
1N
M10
U18
0.2
9-0
.32
180.
3017
8.55
94.1
81.
002
143.
210.
9014
3.22
139.
5194
.06
1.00
2N
M10
C18
0.4
6-0
.20
180.
4817
8.58
94.3
21.
002
143.
271.
0214
3.28
139.
5294
.14
1.00
2N
M20
U18
0.9
9-0
.37
181.
0017
9.34
93.9
81.
006
143.
301.
0714
3.31
140.
2494
.10
1.00
7N
M20
C18
1.3
4-0
.13
181.
3617
9.35
94.1
01.
006
143.
900.
8614
3.91
140.
2693
.90
1.00
7N
M30
U18
3.3
40.
3618
3.36
180.
9394
.20
1.01
514
4.94
1.68
144.
9514
1.52
94.2
21.
016
NM
30C
182.1
20.
7718
2.13
180.
8994
.42
1.01
514
5.26
1.37
145.
2714
1.35
93.8
81.
015
NM
40U
184.2
80.
4618
4.30
183.
2694
.32
1.02
814
5.78
1.85
145.
7814
3.30
94.4
21.
029
NM
40C
184.3
7-0
.38
184.
3918
2.93
94.1
61.
026
146.
271.
2814
6.28
142.
7894
.24
1.02
5N
M50
U18
9.3
8-0
.24
189.
4018
6.52
94.1
01.
046
149.
820.
8514
9.83
145.
6093
.96
1.04
5N
M50
C18
8.8
8-0
.51
188.
9018
5.02
94.4
01.
038
149.
541.
3114
9.55
144.
8793
.80
1.04
0N
M60
U19
3.1
4-0
.34
193.
1519
0.76
94.2
41.
070
152.
491.
3715
2.50
149.
1493
.82
1.07
1N
M60
C18
9.6
10.
4318
9.63
188.
2194
.10
1.05
615
1.02
0.31
151.
0314
7.18
93.9
61.
057
NM
70U
199.3
41.
1319
9.36
196.
1793
.90
1.10
115
9.06
-0.0
015
9.07
153.
7893
.44
1.10
4N
M70
C19
5.0
7-1
.62
195.
0819
1.19
93.8
81.
073
153.
841.
0015
3.85
149.
6793
.90
1.07
5N
M80
U20
7.7
12.
0820
7.72
204.
1493
.90
1.14
516
5.26
0.68
165.
2815
9.88
94.0
61.
148
NM
80C
199.2
20.
0919
9.24
194.
3693
.42
1.09
015
7.14
0.27
157.
1615
2.23
93.9
21.
093
NM
90U
223.6
83.
9822
3.67
217.
4193
.98
1.22
017
2.53
2.11
172.
5417
0.03
94.0
61.
221
NM
90C
201.5
71.
4820
1.58
198.
5694
.04
1.11
415
9.67
1.63
159.
6815
4.99
93.5
61.
113
64
Tab
leE
5:In
fere
nce
for
the
log
scal
em
eanµ
bas
edfu
lly
mas
kedLN
(µ=
0,σ
2=
1)d
ata
Res
ult
sfo
rn
=10
0R
esu
lts
forn
=20
0
RM
SE
Bia
sS
DS
DC
vg.
Rel
.R
MS
EB
ias
SD
SD
Cvg.
Rel
.×
103×
103
×10
3×
103
%L
en.
×10
3×
103×
103×
103
%L
en.
CD
101.6
00.
8410
1.60
99.2
794
.00
1.00
070
.05
0.68
70.0
670
.51
95.1
01.
000
MI
104.0
50.
7510
4.05
102.
2794
.26
1.03
071
.57
0.79
71.5
772
.30
95.2
41.
025
NM
10U
101.7
10.
9210
1.71
99.4
594
.22
1.00
270
.15
0.61
70.1
570
.63
95.2
21.
002
NM
10C
101.8
01.
0510
1.81
99.4
394
.22
1.00
270
.21
0.66
70.2
170
.64
95.0
81.
002
NM
20U
102.5
40.
9810
2.55
99.9
694
.32
1.00
770
.43
0.62
70.4
470
.98
95.1
41.
007
NM
20C
102.2
31.
0410
2.23
99.9
594
.20
1.00
770
.54
0.62
70.5
470
.99
95.1
81.
007
NM
30U
102.9
00.
5510
2.91
100.
7794
.24
1.01
571
.00
0.42
71.0
171
.61
95.2
41.
016
NM
30C
102.8
30.
9010
2.83
100.
7194
.34
1.01
471
.07
0.82
71.0
771
.55
95.3
01.
015
NM
40U
104.3
31.
0010
4.34
102.
0794
.32
1.02
872
.49
0.57
72.5
072
.53
95.2
41.
029
NM
40C
103.4
50.
7810
3.46
101.
8094
.12
1.02
571
.89
0.24
71.9
072
.36
95.4
21.
026
NM
50U
106.5
51.
2810
6.56
103.
8794
.12
1.04
673
.22
0.62
73.2
273
.76
95.1
61.
046
NM
50C
105.1
20.
5910
5.13
103.
1394
.08
1.03
973
.05
0.65
73.0
673
.31
95.1
21.
040
NM
60U
108.2
02.
0310
8.19
106.
2794
.24
1.07
075
.41
0.55
75.4
175
.44
95.1
61.
070
NM
60C
107.5
20.
5010
7.53
104.
8194
.08
1.05
674
.51
0.08
74.5
174
.38
94.8
41.
055
NM
70U
111.4
8-0
.52
111.
4910
9.50
94.0
61.
103
78.3
21.
1778
.32
77.7
994
.66
1.10
3N
M70C
109.2
10.
7910
9.22
106.
4994
.14
1.07
375
.00
0.53
75.0
175
.63
95.2
81.
073
NM
80U
116.5
70.
6311
6.58
114.
0593
.90
1.14
981
.71
0.26
81.7
281
.00
94.8
81.
149
NM
80C
110.1
50.
4611
0.16
108.
4494
.50
1.09
276
.57
1.14
76.5
776
.95
94.7
21.
091
NM
90U
123.5
21.
2412
3.52
121.
1494
.56
1.22
085
.86
-0.1
685
.87
86.0
595
.00
1.22
0N
M90C
112.4
10.
3111
2.42
110.
6394
.26
1.11
477
.98
0.74
77.9
878
.44
95.0
01.
112
65
Tab
leE
6:In
fere
nce
for
the
log
scal
em
eanµ
bas
edfu
lly
mas
kedLN
(µ=
0,σ
2=
1)d
ata
Res
ult
sfo
rn
=10
00R
esu
lts
forn
=20
00
RM
SE
Bia
sS
DS
DC
vg.
Rel
.R
MS
EB
ias
SD
SD
Cvg.
Rel
.×
103
×10
3×
103×
103
%L
en.
×10
3×
103×
103×
103
%L
en.
CD
31.5
80.
5931
.58
31.6
095
.20
1.00
022
.55
0.24
22.5
522
.36
94.8
41.
000
MI
32.0
20.
5432
.02
32.2
695
.10
1.02
123
.03
0.27
23.0
322
.81
94.9
41.
020
NM
10U
31.6
30.
6131
.63
31.6
695
.08
1.00
222
.60
0.26
22.6
022
.40
94.8
21.
002
NM
10C
31.6
30.
6031
.63
31.6
695
.02
1.00
222
.56
0.26
22.5
622
.40
94.9
61.
002
NM
20U
31.8
70.
5131
.87
31.8
295
.20
1.00
722
.70
0.21
22.7
022
.51
94.9
81.
007
NM
20C
31.9
10.
6431
.91
31.8
195
.00
1.00
722
.69
0.20
22.6
922
.51
94.9
01.
007
NM
30U
32.1
30.
6432
.12
32.0
995
.02
1.01
522
.84
0.17
22.8
422
.71
95.0
41.
016
NM
30C
32.1
00.
8032
.09
32.0
795
.28
1.01
522
.86
0.28
22.8
622
.69
94.8
41.
015
NM
40U
32.5
60.
6132
.56
32.5
094
.96
1.02
823
.10
0.16
23.1
123
.00
94.9
01.
028
NM
40C
32.3
10.
6932
.30
32.4
195
.14
1.02
623
.06
0.30
23.0
622
.93
94.9
21.
026
NM
50U
32.9
60.
5632
.95
33.0
895
.26
1.04
723
.53
0.27
23.5
323
.40
94.5
41.
046
NM
50C
32.8
20.
6032
.82
32.8
495
.00
1.03
923
.49
0.21
23.4
923
.24
95.2
21.
039
NM
60U
33.7
50.
7033
.75
33.8
395
.00
1.07
024
.00
0.20
24.0
023
.93
95.1
21.
070
NM
60C
33.2
30.
4433
.24
33.3
595
.10
1.05
523
.65
0.12
23.6
523
.59
94.9
61.
055
NM
70U
34.5
40.
3634
.54
34.8
695
.34
1.10
324
.94
0.04
24.9
424
.66
95.0
41.
103
NM
70C
34.1
50.
6034
.15
33.9
295
.00
1.07
324
.31
-0.0
124
.31
23.9
994
.68
1.07
3N
M80U
36.6
20.
8036
.61
36.3
294
.52
1.14
925
.52
0.42
25.5
225
.69
95.2
81.
149
NM
80C
34.8
00.
5334
.80
34.5
394
.50
1.09
324
.59
0.09
24.6
024
.42
95.0
21.
092
NM
90U
38.5
20.
4938
.52
38.5
594
.94
1.22
027
.60
0.09
27.6
027
.27
94.6
81.
220
NM
90C
35.0
60.
4935
.06
35.1
894
.96
1.11
324
.94
0.43
24.9
424
.89
94.6
81.
113
66
Tab
leE
7:In
fere
nce
for
the
log
scal
eva
rian
ceσ
2b
ased
onfu
lly
mas
kedLN
(µ=
0,σ
2=
1)d
ata
Res
ult
sfo
rn
=30
Res
ult
sfo
rn
=50
RM
SE
Bia
sS
DS
DC
vg.
Rel
.R
MS
EB
ias
SD
SD
Cvg.
Rel
.×
103×
103
×10
3×
103
%L
en.
×10
3×
103
×10
3×
103
%L
en.
CD
257.5
0-3
0.14
255.
7625
0.42
89.6
01.
000
199.
30-1
9.91
198.
3219
6.02
91.4
81.
000
MI
283.0
540
.68
280.
1429
3.92
94.1
41.
174
211.
9521
.45
210.
8921
6.95
94.2
41.
107
NM
10U
258.0
2-3
0.13
256.
2825
1.28
89.5
41.
003
200.
32-2
0.09
199.
3319
6.65
91.3
41.
003
NM
10C
257.8
2-2
9.83
256.
1225
1.36
89.4
81.
004
200.
29-1
9.97
199.
3119
6.67
91.3
21.
003
NM
20U
260.0
3-3
1.82
258.
1025
3.48
89.2
01.
012
202.
43-2
0.00
201.
4619
8.71
91.4
61.
014
NM
20C
261.9
7-3
1.11
260.
1525
3.59
89.7
21.
013
201.
96-1
9.44
201.
0419
8.76
91.5
81.
014
NM
30U
264.2
1-3
2.18
262.
2725
7.93
89.6
41.
030
206.
21-1
9.50
205.
3020
2.32
91.5
81.
032
NM
30C
266.4
0-3
0.53
264.
6825
7.95
89.5
61.
030
204.
69-2
0.33
203.
7020
1.85
91.5
61.
030
NM
40U
272.1
0-3
2.54
270.
1726
4.54
89.3
81.
056
210.
89-2
0.43
209.
9220
7.30
91.5
21.
058
NM
40C
272.0
7-3
0.22
270.
4126
3.81
89.4
81.
053
209.
70-2
2.07
208.
5520
5.98
91.4
81.
051
NM
50U
279.6
7-3
2.89
277.
7527
3.75
90.1
41.
093
215.
93-2
4.10
214.
6121
3.73
91.6
01.
090
NM
50C
279.8
5-3
4.70
277.
7226
9.91
89.1
01.
078
213.
91-2
0.04
213.
0021
2.00
91.8
81.
082
NM
60U
299.2
1-3
4.27
297.
2728
5.98
88.9
61.
142
227.
60-2
2.26
226.
5422
3.82
91.6
21.
142
NM
60C
286.5
5-3
2.00
284.
7827
9.20
89.2
41.
115
221.
25-1
9.18
220.
4421
8.83
91.7
61.
116
NM
70U
309.4
4-4
2.62
306.
5330
0.97
89.4
01.
202
238.
43-2
2.68
237.
3723
7.02
91.5
21.
209
NM
70C
298.1
4-3
5.21
296.
0928
8.17
89.6
01.
151
230.
41-1
9.67
229.
5922
6.32
91.5
01.
155
NM
80U
334.6
6-4
9.35
331.
0332
2.94
88.1
01.
290
260.
19-3
0.19
258.
4625
3.81
90.7
21.
295
NM
80C
305.8
5-4
0.30
303.
2229
7.72
89.5
61.
189
238.
91-2
2.74
237.
8523
4.13
91.3
21.
194
NM
90U
366.8
2-5
2.33
363.
1035
6.45
88.3
81.
423
286.
05-3
0.25
284.
4828
0.63
91.3
01.
432
NM
90C
317.9
5-3
5.60
315.
9831
0.72
89.2
21.
241
247.
29-2
5.57
245.
9824
2.69
91.4
81.
238
67
Tab
leE
8:In
fere
nce
for
the
log
scal
eva
rian
ceσ
2b
ased
onfu
lly
mas
kedLN
(µ=
0,σ
2=
1)d
ata
Res
ult
sfo
rn
=10
0R
esu
lts
forn
=20
0
RM
SE
Bia
sS
DS
DC
vg.
Rel
.R
MS
EB
ias
SD
SD
Cvg.
Rel
.×
103
×10
3×
103
×10
3%
Len
.×
103×
103
×10
3×
103
%L
en.
CD
138
.01
-9.7
213
7.68
140.
0594
.04
1.00
010
2.64
-2.9
010
2.61
99.7
193
.36
1.00
0M
I144
.13
10.6
414
3.75
148.
7195
.28
1.06
210
6.04
7.62
105.
7810
3.76
94.0
81.
041
NM
10U
138
.46
-9.5
913
8.15
140.
5493
.74
1.00
410
2.85
-2.8
710
2.82
100.
0593
.42
1.00
3N
M10C
138
.56
-9.9
213
8.22
140.
4994
.06
1.00
310
2.97
-2.7
910
2.94
100.
0593
.36
1.00
3N
M20U
140
.11
-9.5
313
9.80
141.
9993
.84
1.01
410
4.11
-3.2
510
4.07
101.
0393
.18
1.01
3N
M20C
139
.62
-9.4
713
9.31
141.
9593
.90
1.01
410
3.74
-2.7
810
3.71
101.
0593
.58
1.01
3N
M30U
143
.65
-10.
8614
3.26
144.
2893
.50
1.03
010
6.28
-2.8
710
6.26
102.
8293
.36
1.03
1N
M30C
142
.46
-10.
3814
2.10
144.
1393
.44
1.02
910
6.02
-2.8
210
5.99
102.
6793
.20
1.03
0N
M40U
146
.98
-10.
8314
6.59
147.
9493
.68
1.05
610
8.47
-2.9
310
8.44
105.
4093
.62
1.05
7N
M40C
145
.02
-10.
6014
4.65
147.
2793
.76
1.05
210
7.08
-1.9
010
7.07
105.
0193
.66
1.05
3N
M50U
151
.89
-10.
5115
1.54
153.
0593
.60
1.09
311
1.76
-3.9
211
1.71
108.
8793
.58
1.09
2N
M50C
149
.72
-11.
3414
9.31
151.
1493
.62
1.07
911
1.15
-2.4
111
1.14
107.
7694
.04
1.08
1N
M60U
159
.34
-10.
9115
8.98
159.
8593
.38
1.14
111
7.71
-4.5
211
7.63
113.
6593
.50
1.14
0N
M60C
155
.28
-9.4
315
5.01
156.
1193
.80
1.11
511
3.63
-3.8
211
3.57
110.
9593
.58
1.11
3N
M70U
169
.59
-11.
8816
9.19
169.
0593
.00
1.20
712
3.41
-3.6
312
3.37
120.
3393
.84
1.20
7N
M70C
163
.02
-11.
6016
2.62
161.
1893
.28
1.15
111
7.71
-4.2
211
7.64
114.
7193
.28
1.15
0N
M80U
182
.80
-13.
7218
2.31
181.
8193
.10
1.29
813
1.21
-5.2
513
1.11
129.
3493
.40
1.29
7N
M80C
166
.68
-11.
5416
6.29
167.
1493
.24
1.19
312
1.30
-6.1
612
1.16
118.
7293
.28
1.19
1N
M90U
201
.43
-15.
0620
0.89
201.
0592
.90
1.43
614
8.31
-3.7
214
8.27
143.
2092
.94
1.43
6N
M90C
170
.98
-9.2
417
0.75
173.
9293
.86
1.24
212
6.36
-5.1
312
6.27
123.
3994
.04
1.23
7
68
Tab
leE
9:In
fere
nce
for
the
log
scal
eva
rian
ceσ
2b
ased
onfu
lly
mas
kedLN
(µ=
0,σ
2=
1)d
ata
Res
ult
sfo
rn
=10
00R
esu
lts
forn
=20
00
RM
SE
Bia
sS
DS
DC
vg.
Rel
.R
MS
EB
ias
SD
SD
Cvg.
Rel
.×
103
×10
3×
103×
103
%L
en.
×10
3×
103×
103×
103
%L
en.
CD
45.0
4-0
.63
45.0
444
.69
94.6
41.
000
32.1
70.
2032
.17
31.6
394
.86
1.00
0M
I46.0
81.
4646
.06
45.7
794
.72
1.02
433
.06
1.20
33.0
432
.32
94.7
01.
022
NM
10U
45.2
3-0
.62
45.2
344
.84
94.6
41.
003
32.2
80.
2132
.28
31.7
494
.74
1.00
3N
M10C
45.2
1-0
.54
45.2
144
.85
94.6
61.
003
32.2
70.
2032
.28
31.7
394
.76
1.00
3N
M20U
45.4
5-0
.51
45.4
545
.30
94.6
61.
014
32.3
90.
2132
.40
32.0
695
.02
1.01
4N
M20C
45.5
9-0
.63
45.5
945
.29
94.9
01.
013
32.6
10.
2632
.61
32.0
594
.82
1.01
3N
M30U
46.3
2-0
.87
46.3
246
.07
94.8
81.
031
32.9
50.
1232
.96
32.6
194
.74
1.03
1N
M30C
46.3
7-0
.55
46.3
746
.02
94.8
21.
030
32.9
20.
3032
.92
32.5
794
.62
1.03
0N
M40U
47.7
8-0
.79
47.7
847
.23
94.1
81.
057
33.8
20.
0933
.82
33.4
294
.74
1.05
7N
M40C
47.2
0-0
.75
47.2
047
.01
94.6
21.
052
33.6
70.
0733
.67
33.2
794
.98
1.05
2N
M50U
49.2
9-0
.06
49.3
048
.86
94.4
01.
093
34.8
30.
4934
.83
34.5
794
.88
1.09
3N
M50C
48.3
8-0
.99
48.3
848
.26
94.4
61.
080
34.6
60.
6734
.66
34.1
894
.82
1.08
0N
M60U
51.7
5-0
.95
51.7
450
.98
94.1
01.
141
36.5
20.
2536
.52
36.0
994
.68
1.14
1N
M60C
50.0
0-0
.82
50.0
049
.75
94.8
41.
113
35.8
1-0
.03
35.8
135
.21
95.1
41.
113
NM
70U
54.5
2-1
.42
54.5
053
.90
94.3
81.
206
38.4
6-0
.06
38.4
738
.16
94.7
81.
206
NM
70C
51.5
3-0
.29
51.5
451
.47
95.2
01.
152
36.9
0-0
.02
36.9
136
.41
94.3
41.
151
NM
80U
58.5
0-0
.96
58.4
958
.04
94.9
01.
299
41.7
6-0
.25
41.7
741
.06
94.5
81.
298
NM
80C
53.9
9-0
.31
54.0
053
.36
94.4
21.
194
37.8
40.
0537
.84
37.7
494
.88
1.19
3N
M90U
64.1
6-1
.05
64.1
664
.17
94.7
01.
436
45.9
80.
2845
.98
45.4
194
.86
1.43
6N
M90C
55.7
8-0
.53
55.7
855
.39
94.7
01.
239
40.0
70.
3140
.07
39.1
994
.24
1.23
9
69
Tab
leE
10:
Infe
ren
cefo
rth
em
eaneµ
+σ2/2
bas
edon
full
ym
aske
dLN
(µ=
0,σ
2=
1)d
ata
Res
ult
sfo
rn
=30
Res
ult
sfo
rn
=50
RM
SE
Bia
sS
DS
DC
vg.
Rel
.R
MS
EB
ias
SD
SD
Cvg.
Rel
.×
103
×10
3×
103
×10
3%
Len
.×
103
×10
3×
103
×10
3%
Len
.
CD
378.1
815
.85
377.
8837
1.76
91.0
01.
000
297.
2510
.78
297.
0828
6.92
92.3
21.
000
MI
527.6
719
6.00
489.
9760
0.18
96.1
81.
614
353.
9110
6.84
337.
4336
2.65
96.0
41.
264
NM
10U
378.8
715
.63
378.
5937
2.58
91.0
21.
002
298.
1410
.71
297.
9828
7.56
92.3
21.
002
NM
10C
379.5
516
.18
379.
2537
2.79
91.0
01.
003
298.
3511
.03
298.
1828
7.63
92.3
81.
002
NM
20U
380.2
814
.53
380.
0437
4.54
91.0
81.
007
299.
5411
.30
299.
3628
9.70
92.3
21.
010
NM
20C
384.0
316
.13
383.
7337
5.23
90.8
61.
009
300.
2611
.50
300.
0728
9.78
92.3
41.
010
NM
30U
386.0
116
.58
385.
6937
9.45
90.8
01.
021
304.
9013
.54
304.
6229
3.65
92.4
21.
023
NM
30C
384.5
218
.22
384.
1338
0.01
91.2
41.
022
303.
3312
.14
303.
1129
2.95
92.3
21.
021
NM
40U
391.6
017
.42
391.
2538
6.11
91.0
41.
039
305.
8613
.22
305.
6129
8.20
92.8
61.
039
NM
40C
392.6
818
.22
392.
3038
6.10
91.0
01.
039
307.
5111
.30
307.
3429
6.95
92.2
01.
035
NM
50U
403.9
418
.74
403.
5539
5.03
90.6
41.
063
315.
7810
.44
315.
6430
3.57
91.9
41.
058
NM
50C
403.7
616
.76
403.
4539
2.13
90.8
61.
055
310.
9613
.63
310.
6930
3.14
92.6
61.
057
NM
60U
416.5
820
.13
416.
1340
6.48
90.4
81.
093
323.
9414
.09
323.
6731
2.95
92.0
61.
091
NM
60C
408.7
421
.47
408.
2240
2.53
91.1
61.
083
322.
0914
.44
321.
7931
0.22
92.4
01.
081
NM
70U
431.5
918
.93
431.
2241
7.67
90.3
21.
123
333.
4013
.32
333.
1632
2.92
91.6
61.
125
NM
70C
425.2
019
.30
424.
8141
1.56
90.2
21.
107
332.
2216
.97
331.
8231
8.19
92.1
21.
109
NM
80U
440.4
117
.28
440.
1143
1.57
89.8
41.
161
349.
0411
.19
348.
9033
3.76
91.3
61.
163
NM
80C
429.3
519
.09
428.
9742
0.70
90.0
81.
132
340.
8014
.88
340.
5132
5.47
91.9
01.
134
NM
90U
466.6
124
.08
466.
0445
1.88
89.2
61.
216
357.
6714
.97
357.
3934
8.83
91.5
81.
216
NM
90C
448.0
628
.09
447.
2243
6.24
91.1
81.
173
349.
1016
.19
348.
7633
4.07
91.7
81.
164
70
Tab
leE
11:
Infe
ren
cefo
rth
em
eaneµ
+σ2/2
bas
edon
full
ym
aske
dLN
(µ=
0,σ
2=
1)d
ata
Res
ult
sfo
rn
=10
0R
esu
lts
forn
=20
0
RM
SE
Bia
sS
DS
DC
vg.
Rel
.R
MS
EB
ias
SD
SD
Cvg.
Rel
.×
103×
103
×10
3×
103
%L
en.
×10
3×
103
×10
3×
103
%L
en.
CD
204.5
15.
8620
4.44
202.
4193
.66
1.00
014
2.03
4.77
141.
9614
3.32
94.9
01.
000
MI
224.1
949
.82
218.
6122
6.79
95.7
01.
120
150.
9826
.74
148.
6115
2.96
95.8
61.
067
NM
10U
204.8
66.
1420
4.79
202.
9293
.76
1.00
314
2.30
4.70
142.
2414
3.64
95.0
21.
002
NM
10C
204.9
56.
0920
4.88
202.
8793
.64
1.00
214
2.57
4.88
142.
5014
3.66
94.8
01.
002
NM
20U
206.8
86.
5220
6.80
204.
3793
.64
1.01
014
3.59
4.52
143.
5414
4.56
94.9
01.
009
NM
20C
206.0
56.
5820
5.96
204.
3593
.84
1.01
014
3.09
4.87
143.
0214
4.61
94.7
21.
009
NM
30U
208.4
14.
9220
8.37
206.
3693
.44
1.02
014
5.38
4.65
145.
3214
6.26
94.6
01.
021
NM
30C
207.6
45.
7720
7.59
206.
3693
.62
1.02
014
5.10
5.32
145.
0214
6.22
94.8
61.
020
NM
40U
212.8
86.
2121
2.81
209.
9293
.56
1.03
714
7.66
5.06
147.
5914
8.65
94.8
61.
037
NM
40C
210.6
55.
7821
0.59
209.
4193
.78
1.03
514
6.45
5.24
146.
3714
8.43
94.9
01.
036
NM
50U
216.8
77.
4521
6.76
214.
6093
.56
1.06
014
9.63
4.49
149.
5815
1.65
94.5
81.
058
NM
50C
215.2
85.
4221
5.23
213.
1193
.74
1.05
315
1.46
5.94
151.
3615
1.16
94.6
61.
055
NM
60U
221.7
18.
9322
1.55
220.
4993
.72
1.08
915
5.35
4.40
155.
3115
5.61
94.6
81.
086
NM
60C
220.4
47.
4822
0.34
218.
1593
.80
1.07
815
2.95
4.00
152.
9115
3.99
94.7
61.
074
NM
70U
230.4
75.
1623
0.43
227.
0593
.40
1.12
216
1.69
6.76
161.
5716
0.92
94.6
81.
123
NM
70C
228.0
47.
1522
7.95
223.
0493
.50
1.10
215
6.69
4.72
156.
6415
7.62
94.5
21.
100
NM
80U
241.3
37.
0524
1.26
235.
7793
.06
1.16
516
7.20
4.46
167.
1616
6.59
94.3
01.
162
NM
80C
230.2
56.
9923
0.16
228.
6593
.30
1.13
016
0.87
4.55
160.
8316
1.39
94.3
81.
126
NM
90U
249.8
38.
0124
9.72
245.
7093
.44
1.21
417
3.55
5.71
173.
4717
3.94
94.3
61.
214
NM
90C
235.4
89.
3823
5.32
235.
3893
.56
1.16
316
3.84
5.02
163.
7816
5.80
94.4
41.
157
71
Tab
leE
12:
Infe
ren
cefo
rth
em
eaneµ
+σ2/2
bas
edon
full
ym
aske
dLN
(µ=
0,σ
2=
1)d
ata
Res
ult
sfo
rn
=10
00R
esu
lts
forn
=20
00
RM
SE
Bia
sS
DS
DC
vg.
Rel
.R
MS
EB
ias
SD
SD
Cvg.
Rel
.×
103
×10
3×
103×
103
%L
en.
×10
3×
103×
103×
103
%L
en.
CD
63.7
21.
6963
.70
63.9
395
.28
1.00
046
.10
1.20
46.0
945
.20
94.5
21.
000
MI
65.3
25.
8265
.06
65.7
795
.60
1.02
947
.32
3.33
47.2
046
.30
94.4
61.
024
NM
10U
63.8
81.
7363
.87
64.0
795
.30
1.00
246
.22
1.24
46.2
145
.31
94.4
41.
002
NM
10C
63.8
61.
7963
.85
64.0
895
.30
1.00
246
.11
1.24
46.1
045
.31
94.5
41.
002
NM
20U
64.2
11.
6664
.20
64.5
195
.22
1.00
946
.33
1.17
46.3
245
.61
94.7
21.
009
NM
20C
64.3
31.
7964
.31
64.5
095
.12
1.00
946
.56
1.20
46.5
545
.61
94.5
81.
009
NM
30U
64.9
31.
6164
.92
65.2
295
.36
1.02
046
.88
1.04
46.8
846
.12
94.4
01.
020
NM
30C
65.2
02.
1465
.18
65.2
195
.10
1.02
046
.89
1.38
46.8
746
.10
94.3
81.
020
NM
40U
66.2
51.
6966
.24
66.2
795
.14
1.03
747
.72
1.03
47.7
146
.86
94.3
41.
037
NM
40C
65.9
21.
8465
.90
66.1
495
.32
1.03
547
.70
1.24
47.6
946
.76
94.4
01.
034
NM
50U
67.4
52.
2667
.42
67.7
295
.12
1.05
948
.52
1.56
48.5
047
.87
94.5
21.
059
NM
50C
66.5
81.
5266
.57
67.3
095
.42
1.05
348
.59
1.61
48.5
747
.63
94.5
61.
054
NM
60U
69.3
11.
8269
.29
69.4
495
.04
1.08
650
.04
1.29
50.0
349
.11
94.1
21.
086
NM
60C
67.8
41.
4467
.84
68.7
195
.20
1.07
549
.30
0.91
49.2
948
.58
94.3
01.
075
NM
70U
70.6
70.
9370
.67
71.6
094
.98
1.12
051
.51
0.82
51.5
150
.65
94.5
81.
120
NM
70C
70.3
62.
2470
.33
70.3
594
.86
1.10
050
.79
0.75
50.7
949
.69
94.6
41.
099
NM
80U
73.9
92.
1773
.96
74.3
694
.98
1.16
352
.87
1.33
52.8
652
.56
94.7
01.
163
NM
80C
72.4
22.
2072
.40
72.1
095
.06
1.12
851
.78
1.00
51.7
750
.94
94.5
61.
127
NM
90U
77.3
31.
7577
.32
77.4
694
.86
1.21
255
.72
1.32
55.7
154
.78
94.5
01.
212
NM
90C
74.0
12.
0373
.99
73.9
895
.36
1.15
753
.21
1.82
53.1
952
.31
94.3
81.
157
72
Tab
leE
13:
Infe
ren
cefo
rth
eva
rian
cee2µ
+2σ2−e2µ
+σ2
bas
edon
fully
mas
kedLN
(µ=
0,σ
2=
1)d
ata
Res
ult
sfo
rn
=30
Res
ult
sfo
rn
=50
RM
SE
Bia
sS
DS
DC
vg.
Rel
.R
MS
EB
ias
SD
SD
Cvg.
Rel
.×
103
×103
×10
3×
103
%L
en.
×10
3×
103
×10
3×
103
%L
en.
CD
5464.
0699
0.0
453
74.1
647
24.9
482
.26
1.00
036
16.2
656
2.15
3572
.65
3250
.99
85.6
61.
000
MI
2×
1010
3×
108
2×
1010
2×
1010
97.8
23×
106
2221
1.99
5685
.50
2147
4.17
2744
4.25
96.8
88.
442
NM
10U
5484.
6799
4.0
253
94.3
847
43.1
482
.32
1.00
436
35.9
856
6.53
3591
.93
3264
.36
85.6
41.
004
NM
10C
5489.
3510
00.5
553
97.9
347
47.8
082
.10
1.00
536
46.0
257
0.21
3601
.51
3267
.23
85.7
01.
005
NM
20U
5495.
0498
5.6
054
06.4
747
74.1
881
.48
1.01
036
85.5
758
4.45
3639
.30
3307
.95
85.8
01.
018
NM
20C
5648.
2710
32.9
655
53.5
748
27.6
481
.70
1.02
237
04.5
458
9.24
3657
.74
3310
.79
85.7
81.
018
NM
30U
5723.
7210
41.1
156
28.8
049
06.5
081
.82
1.03
838
36.2
863
3.01
3784
.08
3396
.00
85.5
81.
045
NM
30C
5765.
7110
74.6
756
65.2
349
41.1
882
.04
1.04
637
44.2
060
2.28
3695
.81
3366
.48
85.8
61.
036
NM
40U
6015.
4911
10.9
059
12.6
150
91.8
481
.50
1.07
838
51.5
763
8.69
3798
.62
3473
.16
85.4
21.
068
NM
40C
6062.
5011
46.3
959
53.7
351
16.3
381
.60
1.08
338
43.9
761
6.21
3794
.64
3443
.65
85.3
21.
059
NM
50U
6268.
3111
91.1
461
54.7
153
17.0
281
.68
1.12
539
94.1
263
8.87
3943
.09
3570
.82
84.7
61.
098
NM
50C
6301.
0511
80.1
661
90.1
652
74.8
080
.80
1.11
639
29.8
166
2.51
3873
.95
3560
.72
85.6
01.
095
NM
60U
7353.
5113
98.1
072
20.1
057
94.8
480
.92
1.22
642
82.0
074
7.65
4216
.64
3797
.12
84.8
61.
168
NM
60C
6682.
9613
02.5
065
55.4
655
55.3
681
.52
1.17
642
53.7
675
1.44
4187
.28
3736
.56
85.4
61.
149
NM
70U
7634.
4914
35.3
574
99.1
060
88.8
080
.18
1.28
946
07.5
780
0.36
4537
.98
4018
.59
84.6
21.
236
NM
70C
7082.
9814
11.9
269
41.5
258
55.7
880
.70
1.23
946
41.1
284
0.43
4564
.84
3928
.95
84.9
21.
209
NM
80U
8395.
0515
22.4
282
56.6
865
65.2
379
.70
1.38
951
46.5
588
4.66
5070
.46
4341
.52
83.4
81.
335
NM
80C
7470.
5114
15.9
373
35.8
360
46.7
881
.14
1.28
049
56.7
886
9.69
4880
.38
4086
.03
84.6
21.
257
NM
90U
9161.
2818
30.4
589
77.4
574
67.5
977
.96
1.58
056
60.2
410
41.2
855
64.1
948
26.7
882
.72
1.48
5N
M90C
8440.
4117
07.3
382
66.7
566
10.9
681
.54
1.39
951
05.7
991
7.40
5023
.20
4264
.82
83.6
01.
312
73
Tab
leE
14:
Infe
ren
cefo
rth
eva
rian
cee2µ
+2σ2−e2µ
+σ2
bas
edon
fully
mas
kedLN
(µ=
0,σ
2=
1)d
ata
Res
ult
sfo
rn
=10
0R
esu
lts
forn
=20
0
RM
SE
Bia
sS
DS
DC
vg.
Rel
.R
MS
EB
ias
SD
SD
Cvg.
Rel
.×
103
×10
3×
103
×10
3%
Len
.×
103
×10
3×
103
×10
3%
Len
.
CD
2159
.09
254
.04
2144
.30
2101
.53
90.1
21.
000
1487
.10
157.
2214
78.9
114
42.3
791
.88
1.00
0M
I3536
.33
1627
.36
3139
.95
4214
.81
96.9
42.
006
1927
.71
739.
4517
80.4
219
76.8
196
.64
1.37
1N
M10
U2166
.99
258
.30
2151
.75
2109
.92
89.8
81.
004
1492
.85
157.
8514
84.6
314
46.9
192
.12
1.00
3N
M10
C2167
.72
255
.71
2152
.80
2108
.46
90.0
81.
003
1494
.89
160.
0314
86.4
514
47.6
792
.12
1.00
4N
M20
U2196
.00
267
.78
2179
.83
2133
.84
90.1
41.
015
1509
.26
157.
8615
01.1
314
59.8
591
.84
1.01
2N
M20
C2176
.31
265
.75
2160
.24
2131
.94
90.3
01.
014
1500
.24
161.
5714
91.6
714
60.8
391
.94
1.01
3N
M30
U2240
.86
260
.87
2225
.85
2163
.70
89.6
61.
030
1543
.65
167.
6615
34.6
814
85.8
092
.18
1.03
0N
M30
C2232
.94
264
.55
2217
.44
2162
.65
89.6
21.
029
1535
.95
170.
3915
26.6
214
84.9
991
.96
1.03
0N
M40
U2305
.33
284
.43
2287
.94
2222
.59
89.8
41.
058
1574
.44
174.
9915
64.8
415
20.3
491
.98
1.05
4N
M40
C2277
.00
275
.55
2260
.49
2210
.26
90.0
81.
052
1559
.49
180.
1315
49.2
115
17.4
892
.50
1.05
2N
M50
U2389
.94
312
.17
2369
.70
2301
.67
88.9
61.
095
1604
.96
172.
1515
95.8
615
62.3
691
.56
1.08
3N
M50
C2370
.68
289
.06
2353
.23
2271
.32
89.1
61.
081
1645
.86
196.
2416
34.2
815
59.9
091
.76
1.08
1N
M60
U2507
.79
346
.20
2484
.03
2405
.16
89.2
41.
144
1697
.23
185.
7516
87.2
016
24.8
291
.38
1.12
6N
M60
C2482
.45
338
.15
2459
.56
2362
.17
89.5
81.
124
1640
.05
177.
8916
30.5
415
95.2
392
.00
1.10
6N
M70
U2659
.77
361
.82
2635
.31
2526
.98
87.6
41.
202
1784
.13
224.
4017
70.1
417
13.7
691
.44
1.18
8N
M70
C2621
.48
359
.44
2596
.98
2447
.88
88.6
01.
165
1715
.66
193.
6317
04.8
716
50.1
091
.62
1.14
4N
M80
U2905
.02
419
.25
2874
.89
2707
.91
87.7
01.
289
1881
.03
219.
6718
68.3
418
08.4
291
.30
1.25
4N
M80
C2644
.62
371
.44
2618
.67
2533
.97
88.4
41.
206
1777
.77
191.
5117
67.6
117
02.8
791
.34
1.18
1N
M90
U3159
.05
476
.65
3123
.19
2943
.67
87.2
81.
401
2062
.15
281.
5420
43.0
519
67.9
090
.22
1.36
4N
M90
C2735
.17
424
.22
2702
.34
2651
.43
88.7
81.
262
1826
.14
214.
6018
13.6
717
71.4
291
.18
1.22
8
74
Tab
leE
15:
Infe
ren
cefo
rth
eva
rian
cee2µ
+2σ2−e2µ
+σ2
bas
edon
fully
mas
kedLN
(µ=
0,σ
2=
1)d
ata
Res
ult
sfo
rn
=10
00R
esu
lts
forn
=20
00
RM
SE
Bia
sS
DS
DC
vg.
Rel
.R
MS
EB
ias
SD
SD
Cvg.
Rel
.×
103
×10
3×
103
×10
3%
Len
.×
103×
103
×10
3×
103
%L
en.
CD
624.
7834
.30
623.
9062
1.18
94.6
01.
000
448.
3023
.69
447.
7243
7.80
94.3
81.
000
MI
669.
0813
4.94
655.
4066
8.20
95.9
21.
076
471.
5573
.37
465.
8545
8.41
94.8
21.
047
NM
10U
626.
8534
.78
625.
9562
3.09
94.5
81.
003
449.
8324
.11
449.
2343
9.14
94.4
61.
003
NM
10C
627.
0035
.76
626.
0462
3.25
94.6
01.
003
449.
1023
.90
448.
5143
9.11
94.2
01.
003
NM
20U
629.
9335
.50
628.
9962
8.79
94.6
41.
012
450.
9223
.71
450.
3544
3.02
94.6
21.
012
NM
20C
631.
7135
.47
630.
7862
8.63
94.4
41.
012
454.
1124
.54
453.
4944
3.03
94.6
41.
012
NM
30U
639.
3833
.49
638.
5763
7.90
94.3
81.
027
457.
8322
.83
457.
3144
9.59
94.6
21.
027
NM
30C
643.
4739
.21
642.
3463
8.18
94.5
61.
027
457.
7626
.08
457.
0644
9.51
94.6
01.
027
NM
40U
658.
3636
.42
657.
4265
2.12
94.3
61.
050
468.
9423
.42
468.
4045
9.32
93.9
41.
049
NM
40C
654.
2037
.16
653.
2165
0.17
94.7
61.
047
468.
2724
.33
467.
6945
7.97
94.3
01.
046
NM
50U
678.
5746
.95
677.
0167
2.48
94.5
81.
083
481.
1730
.13
480.
2747
3.15
94.3
81.
081
NM
50C
662.
7934
.43
661.
9666
5.15
94.8
01.
071
480.
9831
.74
479.
9846
9.74
94.5
01.
073
NM
60U
704.
4840
.71
703.
3869
5.62
94.2
61.
120
501.
2628
.43
500.
5049
0.02
94.4
61.
119
NM
60C
682.
7337
.28
681.
7868
3.97
94.5
21.
101
491.
6623
.57
491.
1448
1.64
94.1
41.
100
NM
70U
726.
7834
.95
726.
0172
5.96
93.9
61.
169
519.
3025
.01
518.
7551
1.64
94.5
81.
169
NM
70C
711.
4848
.50
709.
9070
6.76
95.1
21.
138
507.
7623
.97
507.
2549
6.39
94.1
61.
134
NM
80U
773.
6150
.04
772.
0776
9.36
94.4
81.
239
550.
3329
.01
549.
6254
0.72
94.3
01.
235
NM
80C
741.
4151
.57
739.
6973
0.52
94.6
21.
176
520.
1826
.95
519.
5451
3.00
94.6
61.
172
NM
90U
827.
0353
.58
825.
3782
3.99
93.8
61.
326
590.
6936
.25
589.
6357
9.55
94.0
61.
324
NM
90C
766.
0151
.88
764.
3375
5.69
94.2
21.
217
545.
6935
.58
544.
5953
1.74
94.3
21.
215
75
Tab
leE
16:
Infe
ren
cefo
rth
e84
thp
erce
nti
leeµ
+σ
bas
edon
fully
mas
kedLN
(µ=
0,σ
2=
1)d
ata
Res
ult
sfo
rn
=30
Res
ult
sfo
rn
=50
RM
SE
Bia
sS
DS
DC
vg.
Rel
.R
MS
EB
ias
SD
SD
Cvg.
Rel
.×
103
×10
3×
103
×10
3%
Len
.×
103
×10
3×
103
×10
3%
Len
.
CD
614.8
12.
6661
4.87
604.
3790
.88
1.00
048
6.00
3.89
486.
0446
9.27
92.2
41.
000
MI
747.0
621
4.82
715.
5880
1.30
95.4
21.
326
545.
8112
4.34
531.
5155
3.13
95.3
41.
179
NM
10U
615.8
92.
2261
5.95
605.
6990
.80
1.00
248
7.47
3.63
487.
5147
0.28
92.0
81.
002
NM
10C
617.0
53.
1461
7.10
606.
0090
.90
1.00
348
7.74
4.17
487.
7747
0.39
92.2
01.
002
NM
20U
618.5
00.
0061
8.56
608.
9590
.98
1.00
848
9.57
4.31
489.
6047
3.69
92.0
81.
009
NM
20C
624.0
92.
2562
4.15
609.
7690
.68
1.00
949
0.65
4.70
490.
6747
3.81
92.0
41.
010
NM
30U
627.1
92.
5862
7.25
616.
6990
.62
1.02
049
7.85
7.43
497.
8447
9.94
92.2
21.
023
NM
30C
624.2
54.
8662
4.30
617.
2691
.02
1.02
149
5.70
5.36
495.
7247
8.97
92.3
41.
021
NM
40U
635.6
62.
4463
5.72
627.
0290
.94
1.03
749
9.66
6.23
499.
6848
7.33
92.7
61.
038
NM
40C
636.7
13.
6963
6.77
626.
6990
.80
1.03
750
2.63
3.22
502.
6748
5.45
92.1
41.
034
NM
50U
656.0
83.
0665
6.14
641.
0590
.48
1.06
151
6.10
0.87
516.
1549
6.19
91.6
81.
057
NM
50C
655.1
6-0
.26
655.
2363
6.45
90.8
01.
053
507.
886.
4450
7.89
495.
3292
.54
1.05
6N
M60U
673.7
01.
1067
3.77
658.
0089
.98
1.08
952
8.67
5.03
528.
7051
0.81
91.8
61.
089
NM
60C
662.1
76.
0966
2.21
652.
6691
.00
1.08
052
5.11
6.61
525.
1250
6.41
92.2
21.
079
NM
70U
697.7
7-3
.54
697.
8367
6.24
90.0
41.
119
544.
051.
9054
4.10
526.
6691
.64
1.12
2N
M70C
687.8
6-0
.04
687.
9266
6.63
90.0
21.
103
540.
659.
2954
0.62
519.
0291
.94
1.10
6N
M80U
713.7
0-1
2.34
713.
6769
7.44
89.4
21.
154
568.
36-5
.53
568.
3954
3.64
91.1
81.
158
NM
80C
695.1
6-2
.11
695.
2368
1.91
90.0
01.
128
554.
494.
4255
4.52
530.
8391
.72
1.13
1N
M90U
755.2
5-1
0.35
755.
2572
6.01
88.4
21.
201
581.
85-4
.40
581.
8956
6.27
91.1
81.
207
NM
90C
722.2
09.
5372
2.21
705.
4891
.06
1.16
756
8.22
5.07
568.
2654
4.83
91.6
81.
161
76
Tab
leE
17:
Infe
ren
cefo
rth
e84
thp
erce
nti
leeµ
+σ
bas
edon
fully
mas
kedLN
(µ=
0,σ
2=
1)d
ata
Res
ult
sfo
rn
=10
0R
esu
lts
forn
=20
0
RM
SE
Bia
sS
DS
DC
vg.
Rel
.R
MS
EB
ias
SD
SD
Cvg.
Rel
.×
103×
103
×10
3×
103
%L
en.
×10
3×
103
×10
3×
103
%L
en.
CD
335.8
63.
1133
5.88
332.
4793
.74
1.00
023
3.51
4.27
233.
4923
5.72
94.9
41.
000
MI
358.7
659
.64
353.
8136
2.73
95.2
01.
091
244.
7733
.12
242.
5524
8.59
95.4
81.
055
NM
10U
336.4
33.
5333
6.45
333.
3093
.70
1.00
223
3.93
4.13
233.
9223
6.24
95.0
01.
002
NM
10C
336.5
73.
4333
6.59
333.
2393
.62
1.00
223
4.38
4.43
234.
3623
6.28
94.6
61.
002
NM
20U
339.7
44.
0033
9.75
335.
6593
.64
1.01
023
6.11
3.74
236.
1123
7.77
94.9
41.
009
NM
20C
338.4
34.
1533
8.43
335.
6293
.82
1.00
923
5.26
4.34
235.
2423
7.83
94.6
81.
009
NM
30U
342.1
71.
0034
2.20
338.
9293
.28
1.01
923
8.98
3.80
238.
9824
0.52
94.5
61.
020
NM
30C
340.9
22.
5334
0.94
338.
9393
.64
1.01
923
8.56
4.93
238.
5324
0.46
94.8
41.
020
NM
40U
349.5
12.
8034
9.53
344.
6993
.48
1.03
724
2.67
4.31
242.
6624
4.43
94.8
81.
037
NM
40C
345.8
72.
3034
5.90
343.
9093
.66
1.03
424
0.63
4.72
240.
6124
4.05
94.9
01.
035
NM
50U
355.8
24.
3435
5.83
352.
2893
.64
1.06
024
5.99
3.13
246.
0024
9.37
94.5
81.
058
NM
50C
353.1
91.
2135
3.22
349.
9293
.66
1.05
224
8.68
5.56
248.
6424
8.50
94.6
81.
054
NM
60U
363.6
45.
9536
3.62
361.
8193
.66
1.08
825
5.29
2.51
255.
3025
5.84
94.6
81.
085
NM
60C
361.4
34.
0136
1.44
357.
9893
.68
1.07
725
1.49
2.18
251.
5025
3.20
94.7
41.
074
NM
70U
378.2
3-1
.42
378.
2737
2.36
93.5
61.
120
265.
645.
9226
5.60
264.
4594
.62
1.12
2N
M70C
373.7
42.
6137
3.77
365.
9493
.46
1.10
125
7.52
3.04
257.
5325
9.15
94.6
21.
099
NM
80U
395.4
90.
0439
5.53
386.
3692
.86
1.16
227
4.67
1.44
274.
7027
3.74
94.3
41.
161
NM
80C
377.6
91.
9637
7.72
375.
1093
.30
1.12
826
4.31
2.45
264.
3326
5.40
94.4
01.
126
NM
90U
409.1
2-1
.01
409.
1640
2.08
93.2
61.
209
284.
981.
9028
5.00
285.
4094
.36
1.21
1N
M90C
386.2
55.
3938
6.25
385.
9193
.54
1.16
126
9.29
2.80
269.
3027
2.55
94.4
61.
156
77
Tab
leE
18:
Infe
ren
cefo
rth
e84
thp
erce
nti
leeµ
+σ
bas
edon
fully
mas
kedLN
(µ=
0,σ
2=
1)d
ata
Res
ult
sfo
rn
=10
00R
esu
lts
forn
=20
00
RM
SE
Bia
sS
DS
DC
vg.
Rel
.R
MS
EB
ias
SD
SD
Cvg.
Rel
.×
103×
103
×10
3×
103
%L
en.
×10
3×
103×
103×
103
%L
en.
CD
104.9
82.
0910
4.97
105.
3595
.26
1.00
075
.98
1.63
75.9
774
.51
94.5
41.
000
MI
107.3
27.
5110
7.07
108.
1495
.50
1.02
677
.86
4.44
77.7
576
.23
94.4
01.
023
NM
10U
105.2
72.
1510
5.25
105.
5995
.26
1.00
276
.18
1.70
76.1
774
.67
94.3
81.
002
NM
10C
105.2
22.
2510
5.21
105.
6095
.28
1.00
275
.99
1.69
75.9
874
.67
94.5
21.
002
NM
20U
105.8
02.
0410
5.79
106.
3095
.12
1.00
976
.35
1.57
76.3
475
.17
94.7
81.
009
NM
20C
105.9
92.
2410
5.98
106.
2995
.08
1.00
976
.73
1.62
76.7
375
.16
94.6
41.
009
NM
30U
107.0
01.
9210
7.00
107.
4895
.38
1.02
077
.28
1.34
77.2
776
.01
94.3
61.
020
NM
30C
107.4
32.
8010
7.40
107.
4695
.08
1.02
077
.28
1.90
77.2
775
.98
94.4
21.
020
NM
40U
109.1
62.
0010
9.16
109.
2195
.06
1.03
778
.65
1.31
78.6
577
.23
94.3
21.
037
NM
40C
108.6
02.
2810
8.58
108.
9995
.28
1.03
578
.62
1.66
78.6
177
.07
94.4
41.
034
NM
50U
111.1
02.
8911
1.08
111.
5895
.08
1.05
979
.95
2.16
79.9
278
.89
94.5
01.
059
NM
50C
109.7
11.
7010
9.71
110.
9195
.40
1.05
380
.06
2.25
80.0
478
.49
94.5
21.
053
NM
60U
114.1
92.
0911
4.19
114.
4395
.06
1.08
682
.47
1.67
82.4
680
.93
94.0
61.
086
NM
60C
111.7
81.
5211
1.78
113.
2295
.16
1.07
581
.26
1.06
81.2
680
.06
94.2
61.
075
NM
70U
116.4
70.
5311
6.48
117.
9894
.98
1.12
084
.90
0.86
84.9
183
.47
94.5
41.
120
NM
70C
115.8
82.
7911
5.85
115.
9294
.88
1.10
083
.71
0.77
83.7
181
.90
94.6
21.
099
NM
80U
121.8
62.
4112
1.84
122.
5195
.00
1.16
387
.13
1.60
87.1
386
.62
94.7
01.
163
NM
80C
119.2
82.
6311
9.27
118.
8095
.00
1.12
885
.34
1.17
85.3
483
.96
94.5
61.
127
NM
90U
127.4
41.
4812
7.44
127.
6194
.86
1.21
191
.82
1.46
91.8
190
.26
94.4
41.
212
NM
90C
121.9
02.
2912
1.89
121.
8995
.34
1.15
787
.69
2.45
87.6
786
.21
94.3
81.
157
78
Tab
leE
19:
Infe
ren
cefo
rth
e95
thp
erce
nti
leeµ
+1.6
45σ
bas
edon
full
ym
aske
dLN
(µ=
0,σ
2=
1)d
ata
Res
ult
sfo
rn
=30
Res
ult
sfo
rn
=50
RM
SE
Bia
sS
DS
DC
vg.
Rel
.R
MS
EB
ias
SD
SD
Cvg.
Rel
.×
103
×10
3×
103
×10
3%
Len
.×
103
×10
3×
103
×10
3%
Len
.
CD
1490.7
61.
2014
90.9
114
57.6
489
.12
1.00
011
64.6
12.
5411
64.7
311
26.5
291
.12
1.00
0M
I20
15.3
9691
.68
1893
.17
2268
.36
95.5
41.
556
1386
.66
380.
0113
33.7
114
40.4
895
.24
1.27
9N
M10
U14
93.4
50.
5614
93.6
014
61.4
589
.12
1.00
311
69.0
32.
0611
69.1
511
29.4
490
.98
1.00
3N
M10
C14
95.9
92.
9414
96.1
414
62.3
688
.88
1.00
311
69.5
43.
2811
69.6
511
29.7
691
.06
1.00
3N
M20
U15
00.7
2-5
.78
1500
.86
1470
.58
89.0
41.
009
1177
.00
4.13
1177
.11
1139
.26
90.9
81.
011
NM
20C
1517.9
50.
9715
18.1
014
73.4
688
.90
1.01
111
78.2
85.
6311
78.3
911
39.6
491
.22
1.01
2N
M30
U15
24.2
5-0
.01
1524
.41
1492
.78
88.9
81.
024
1200
.65
12.2
312
00.7
011
57.2
590
.94
1.02
7N
M30
C15
23.7
97.
3515
23.9
214
95.0
589
.16
1.02
611
91.1
76.
1511
91.2
711
54.1
891
.10
1.02
5N
M40
U15
54.8
01.
6515
54.9
515
23.3
088
.90
1.04
512
07.9
48.
8112
08.0
311
78.3
891
.12
1.04
6N
M40
C15
60.1
88.
4515
60.3
115
23.1
188
.78
1.04
512
12.9
50.
7912
13.0
711
72.7
490
.56
1.04
1N
M50
U16
03.2
25.
7416
03.3
715
64.6
588
.54
1.07
312
46.6
2-5
.08
1246
.74
1203
.75
90.5
81.
069
NM
50C
1604.9
6-3
.24
1605
.12
1550
.96
88.3
21.
064
1225
.10
10.4
012
25.1
812
01.2
591
.18
1.06
6N
M60
U16
73.1
45.
9816
73.3
016
17.3
188
.44
1.11
012
88.7
48.
5712
88.8
412
47.3
690
.48
1.10
7N
M60
C16
31.9
715
.78
1632
.05
1598
.46
88.7
81.
097
1277
.33
15.8
212
77.3
612
34.0
990
.90
1.09
5N
M70
U17
33.6
7-1
2.55
1733
.80
1670
.96
88.1
21.
146
1328
.07
3.66
1328
.20
1295
.26
90.2
61.
150
NM
70C
1704.6
45.
1117
04.8
016
40.4
188
.70
1.12
513
24.1
323
.39
1324
.06
1270
.89
90.6
21.
128
NM
80U
1784.1
5-3
7.01
1783
.94
1738
.89
87.1
61.
193
1407
.13
-17.
5114
07.1
613
48.2
989
.90
1.19
7N
M80
C17
20.4
7-6
.53
1720
.63
1683
.01
88.3
21.
155
1362
.23
11.6
913
62.3
213
05.1
590
.80
1.15
9N
M90
U19
01.6
4-3
0.66
1901
.59
1838
.02
86.1
41.
261
1458
.75
-12.
9314
58.8
314
23.9
389
.62
1.26
4N
M90
C18
06.2
329
.62
1806
.17
1754
.07
88.9
21.
203
1401
.73
10.8
514
01.8
313
45.3
890
.52
1.19
4
79
Tab
leE
20:
Infe
ren
cefo
rth
e95
thp
erce
nti
leeµ
+1.6
45σ
bas
edon
full
ym
aske
dLN
(µ=
0,σ
2=
1)d
ata
Res
ult
sfo
rn
=10
0R
esu
lts
forn
=20
0
RM
SE
Bia
sS
DS
DC
vg.
Rel
.R
MS
EB
ias
SD
SD
Cvg.
Rel
.×
103
×10
3×
103
×10
3%
Len
.×
103×
103
×10
3×
103
%L
en.
CD
795.
672.
8179
5.75
795.
6693
.28
1.00
056
3.07
10.1
556
3.03
563.
8994
.16
1.00
0M
I873.
6017
7.22
855.
5290
0.05
95.7
81.
131
598.
9797
.82
590.
9960
4.98
95.5
61.
073
NM
10U
797.
463.
9079
7.53
798.
0193
.44
1.00
356
4.33
9.97
564.
3056
5.37
94.1
61.
003
NM
10C
797.
743.
1679
7.81
797.
7693
.24
1.00
356
5.35
10.7
256
5.30
565.
4794
.16
1.00
3N
M20
U805.
925.
2080
5.98
804.
6993
.34
1.01
157
0.56
8.83
570.
5556
9.68
94.2
01.
010
NM
20C
802.
575.
4880
2.63
804.
6093
.46
1.01
156
7.82
10.6
456
7.78
569.
8994
.18
1.01
1N
M30
U816.
30-2
.14
816.
3881
4.02
93.1
61.
023
579.
639.
8757
9.61
577.
5894
.14
1.02
4N
M30
C811.
741.
2681
1.82
813.
9893
.24
1.02
357
7.78
12.0
157
7.71
577.
3493
.96
1.02
4N
M40
U835.
342.
1583
5.42
830.
5093
.32
1.04
458
8.54
10.9
358
8.49
588.
6994
.26
1.04
4N
M40
C825.
831.
1982
5.91
828.
1693
.44
1.04
158
2.97
13.2
458
2.88
587.
6894
.26
1.04
2N
M50
U853.
266.
2485
3.32
852.
3393
.02
1.07
159
9.17
7.38
599.
1860
2.78
93.9
41.
069
NM
50C
847.
22-1
.17
847.
3084
5.41
93.2
01.
063
606.
4514
.85
606.
3260
0.34
94.4
41.
065
NM
60U
879.
229.
8887
9.26
880.
0593
.34
1.10
662
5.60
6.07
625.
6462
1.56
94.0
01.
102
NM
60C
870.
488.
2387
0.52
868.
8292
.86
1.09
261
2.51
6.18
612.
5461
3.71
94.1
01.
088
NM
70U
921.
83-3
.56
921.
9291
1.93
92.5
81.
146
652.
7014
.90
652.
6064
6.95
94.2
41.
147
NM
70C
908.
204.
0190
8.28
891.
7092
.84
1.12
163
2.09
7.92
632.
1063
0.73
93.7
81.
119
NM
80U
972.
78-1
.46
972.
8895
4.64
92.0
81.
200
678.
564.
3767
8.61
675.
1993
.74
1.19
7N
M80
C919.
133.
5291
9.21
918.
1392
.88
1.15
465
0.41
4.24
650.
4664
8.48
93.6
21.
150
NM
90U
101
8.3
7-4
.36
1018
.47
1006
.19
92.5
01.
265
718.
559.
3071
8.56
713.
2293
.40
1.26
5N
M90
C941.
6414
.97
941.
6294
9.73
92.9
41.
194
666.
307.
1866
6.33
669.
3293
.98
1.18
7
80
Tab
leE
21:
Infe
ren
cefo
rth
e95
thp
erce
nti
leeµ
+1.6
45σ
bas
edon
full
ym
aske
dLN
(µ=
0,σ
2=
1)d
ata
Res
ult
sfo
rn
=10
00R
esu
lts
forn
=20
00
RM
SE
Bia
sS
DS
DC
vg.
Rel
.R
MS
EB
ias
SD
SD
Cvg.
Rel
.×
103×
103
×10
3×
103
%L
en.
×10
3×
103
×10
3×
103
%L
en.
CD
251.2
34.
3125
1.22
251.
5995
.18
1.00
018
1.90
4.18
181.
8717
7.93
94.3
21.
000
MI
257.9
920
.96
257.
1625
9.12
95.4
41.
030
186.
9412
.61
186.
5318
2.35
94.7
01.
025
NM
10U
252.0
44.
4425
2.03
252.
2695
.18
1.00
318
2.43
4.33
182.
4017
8.40
94.3
21.
003
NM
10C
251.9
34.
7725
1.91
252.
2995
.14
1.00
318
2.04
4.28
182.
0117
8.39
94.2
41.
003
NM
20U
253.1
64.
4225
3.15
254.
2895
.10
1.01
118
2.81
4.09
182.
7817
9.81
94.5
41.
011
NM
20C
253.7
34.
6025
3.71
254.
2394
.98
1.01
018
4.03
4.29
184.
0017
9.79
94.3
61.
010
NM
30U
256.6
73.
6425
6.67
257.
6095
.26
1.02
418
5.48
3.53
185.
4718
2.18
94.6
81.
024
NM
30C
257.8
95.
8725
7.85
257.
5494
.80
1.02
418
5.40
4.90
185.
3518
2.10
94.3
01.
023
NM
40U
263.0
54.
0326
3.04
262.
5394
.86
1.04
318
9.45
3.47
189.
4418
5.64
94.3
21.
043
NM
40C
261.4
94.
6226
1.48
261.
8995
.14
1.04
118
9.25
4.08
189.
2318
5.18
94.5
21.
041
NM
50U
269.0
87.
0326
9.01
269.
3295
.20
1.07
019
3.14
5.78
193.
0719
0.38
94.4
41.
070
NM
50C
264.5
73.
1326
4.58
267.
3395
.20
1.06
319
3.29
6.25
193.
2018
9.23
94.4
81.
064
NM
60U
278.1
34.
1527
8.12
277.
5294
.72
1.10
320
0.49
4.53
200.
4619
6.28
94.3
21.
103
NM
60C
271.0
23.
1727
1.03
273.
9395
.26
1.08
919
7.27
2.88
197.
2719
3.69
94.1
61.
089
NM
70U
285.6
80.
5028
5.71
287.
9395
.04
1.14
420
7.00
2.53
207.
0120
3.72
94.5
81.
145
NM
70C
281.2
36.
6228
1.18
281.
6695
.30
1.12
020
3.38
2.41
203.
3919
8.96
94.5
21.
118
NM
80U
300.0
85.
0230
0.07
301.
5895
.06
1.19
921
5.73
3.73
215.
7221
3.18
94.6
01.
198
NM
80C
291.5
76.
4829
1.52
289.
9495
.12
1.15
220
8.02
3.34
208.
0120
4.85
94.6
21.
151
NM
90U
317.4
23.
3631
7.44
317.
8794
.72
1.26
322
8.64
4.46
228.
6222
4.84
94.5
61.
264
NM
90C
299.7
65.
6229
9.74
298.
8494
.94
1.18
821
6.01
6.32
215.
9421
1.33
94.3
61.
188
81
Tab
leE
22:
Infe
ren
cefo
rth
em
eanµ
bas
edon
full
ym
aske
dN
(µ=
0,σ
2=
1)d
ata
Res
ult
sfo
rn
=30
Res
ult
sfo
rn
=50
RM
SE
Bia
sS
DS
DC
vg.
Rel
.R
MS
EB
ias
SD
SD
Cvg.
Rel
.×
103
×10
3×
103
×10
3%
Len
.×
103×
103
×10
3×
103
%L
en.
CD
181.
900.
4618
1.91
177.
4193
.56
1.00
013
9.82
4.71
139.
7613
9.02
94.4
81.
000
MI
185.
63-0
.02
185.
6518
7.70
94.8
21.
058
142.
574.
9414
2.50
144.
7695
.12
1.04
1N
M10
182.
270.
7118
2.28
177.
7993
.74
1.00
214
0.04
4.81
139.
9713
9.29
94.3
61.
002
NM
20
183.
180.
2218
3.20
178.
8993
.72
1.00
814
0.74
4.63
140.
6814
0.02
94.4
41.
007
NM
30
184.
200.
6318
4.22
180.
1693
.82
1.01
514
1.70
4.73
141.
6314
1.07
94.6
21.
015
NM
40
185.
471.
2418
5.48
181.
9594
.00
1.02
614
2.37
4.84
142.
3014
2.45
94.8
81.
025
NM
50
187.
620.
1818
7.64
183.
9693
.96
1.03
714
4.45
4.51
144.
3914
3.80
94.4
81.
034
NM
60
187.
321.
5318
7.34
185.
5093
.94
1.04
614
5.46
5.26
145.
3814
5.26
94.8
21.
045
NM
70
191.
591.
0619
1.60
188.
3094
.24
1.06
114
7.70
3.32
147.
6814
7.07
95.0
81.
058
NM
80
193.
670.
4919
3.69
190.
4294
.02
1.07
314
8.09
3.88
148.
0614
8.63
94.7
21.
069
NM
90
194.
42-0
.27
194.
4419
2.64
94.3
01.
086
151.
634.
5015
1.57
150.
4995
.22
1.08
3
82
Tab
leE
23:
Infe
ren
cefo
rth
em
eanµ
bas
edon
full
ym
aske
dN
(µ=
0,σ
2=
1)d
ata
Res
ult
sfo
rn
=10
0R
esu
lts
forn
=20
0
RM
SE
Bia
sS
DS
DC
vg.
Rel
.R
MS
EB
ias
SD
SD
Cvg.
Rel
.×
103
×10
3×
103
×10
3%
Len
.×
103×
103×
103×
103
%L
en.
CD
98.7
8-0
.57
98.7
899
.22
94.8
61.
000
69.7
7-0
.35
69.7
870
.43
95.2
61.
000
MI
101.
12-0
.94
101.
1310
2.22
94.9
01.
030
71.5
6-0
.26
71.5
772
.20
95.2
21.
025
NM
1098
.87
-0.3
898
.88
99.3
894
.72
1.00
269
.96
-0.3
369
.97
70.5
595
.26
1.00
2N
M20
99.1
5-0
.32
99.1
699
.91
95.1
21.
007
70.3
2-0
.30
70.3
370
.90
95.4
21.
007
NM
30100.
33-0
.49
100.
3410
0.60
94.8
61.
014
70.8
8-0
.36
70.8
971
.42
95.4
01.
014
NM
40101.
08-0
.40
101.
0910
1.48
94.8
01.
023
71.2
4-0
.20
71.2
571
.98
95.2
61.
022
NM
50101.
94-0
.74
101.
9510
2.43
95.0
01.
032
72.0
3-0
.32
72.0
472
.68
95.3
01.
032
NM
60103.
17-0
.62
103.
1810
3.68
94.7
41.
045
72.5
5-0
.13
72.5
673
.48
95.4
21.
043
NM
70104.
45-1
.64
104.
4410
4.90
95.0
21.
057
74.0
9-0
.21
74.1
074
.40
94.9
81.
056
NM
80105.
86-0
.70
105.
8710
6.10
95.0
01.
069
74.1
10.
0574
.12
75.2
095
.32
1.06
8N
M90
106.
67-1
.21
106.
6710
7.35
95.2
61.
082
75.1
7-0
.48
75.1
876
.21
95.0
01.
082
83
Tab
leE
24:
Infe
ren
cefo
rth
em
eanµ
bas
edon
full
ym
aske
dN
(µ=
0,σ
2=
1)d
ata
Res
ult
sfo
rn
=10
00R
esu
lts
forn
=20
00
RM
SE
Bia
sS
DS
DC
vg.
Rel
.R
MS
EB
ias
SD
SD
Cvg.
Rel
.×
103×
103×
103×
103
%L
en.
×10
3×
103×
103×
103
%L
en.
CD
31.
440.
5531
.44
31.5
994
.78
1.00
021
.67
-0.2
021
.67
22.3
595
.58
1.00
0M
I32.
140.
6532
.13
32.2
594
.92
1.02
122
.11
-0.1
422
.11
22.8
195
.38
1.02
0N
M10
31.
490.
5231
.49
31.6
594
.80
1.00
221
.68
-0.2
021
.68
22.3
995
.56
1.00
2N
M20
31.
620.
5131
.62
31.7
994
.94
1.00
621
.80
-0.1
921
.80
22.4
995
.46
1.00
6N
M30
31.
830.
5831
.83
32.0
194
.90
1.01
321
.96
-0.2
121
.96
22.6
495
.70
1.01
3N
M40
32.
250.
5132
.25
32.2
994
.62
1.02
222
.10
-0.2
922
.10
22.8
495
.90
1.02
2N
M50
32.
470.
5832
.47
32.6
094
.62
1.03
222
.27
-0.1
922
.27
23.0
595
.40
1.03
1N
M60
32.
830.
3632
.83
32.9
394
.64
1.04
222
.66
-0.2
322
.66
23.3
195
.58
1.04
3N
M70
33.
270.
4133
.27
33.3
194
.62
1.05
422
.84
-0.1
122
.84
23.5
795
.66
1.05
4N
M80
33.
570.
4633
.57
33.7
295
.02
1.06
723
.22
-0.1
423
.22
23.8
595
.36
1.06
7N
M90
34.
020.
3234
.02
34.1
894
.76
1.08
223
.64
-0.2
423
.64
24.1
695
.16
1.08
1
84
Tab
leE
25:
Infe
ren
cefo
rth
eva
rian
ceσ
2b
ased
onfu
lly
mas
kedN
(µ=
0,σ
2=
1)d
ata
Res
ult
sfo
rn
=30
Res
ult
sfo
rn
=50
RM
SE
Bia
sS
DS
DC
vg.
Rel
.R
MS
EB
ias
SD
SD
Cvg.
Rel
.×
103
×10
3×
103
×10
3%
Len
.×
103×
103
×10
3×
103
%L
en.
CD
258.
83-3
8.93
255.
9124
8.15
88.8
81.
000
194.
38-2
4.12
192.
9019
5.18
91.8
41.
000
MI
284.
6533
.87
282.
6629
1.93
93.7
21.
176
207.
0617
.15
206.
3721
6.01
94.9
01.
107
NM
10261.
82-3
7.77
259.
1125
0.75
89.0
21.
011
195.
49-2
3.53
194.
0819
7.14
91.9
41.
010
NM
20269.
30-3
4.30
267.
1425
8.11
89.4
01.
040
201.
86-2
1.91
200.
6920
2.54
91.7
21.
038
NM
30278.
33-3
3.53
276.
3326
7.77
89.0
21.
079
208.
21-2
0.45
207.
2321
0.23
91.7
61.
077
NM
40287.
98-3
0.60
286.
3828
0.02
89.6
81.
128
215.
45-1
7.92
214.
7221
9.61
91.9
61.
125
NM
50302.
08-2
7.72
300.
8429
3.58
89.4
21.
183
229.
13-1
7.83
228.
4622
9.41
92.0
21.
175
NM
60315.
28-3
1.64
313.
7230
5.79
89.0
01.
232
234.
86-1
8.84
234.
1323
9.54
92.1
41.
227
NM
70336.
49-2
3.37
335.
7132
2.51
88.9
21.
300
248.
53-1
6.26
248.
0225
1.01
90.9
61.
286
NM
80342.
53-2
5.39
341.
6333
6.18
88.1
01.
355
262.
63-1
8.33
262.
0226
1.57
90.6
41.
340
NM
90351.
31-2
8.46
350.
1934
9.56
88.4
81.
409
270.
38-1
9.92
269.
6727
2.56
91.4
01.
396
85
Tab
leE
26:
Infe
ren
cefo
rth
eva
rian
ceσ
2b
ased
onfu
lly
mas
kedN
(µ=
0,σ
2=
1)d
ata
Res
ult
sfo
rn
=10
0R
esu
lts
forn
=20
0
RM
SE
Bia
sS
DS
DC
vg.
Rel
.R
MS
EB
ias
SD
SD
Cvg.
Rel
.×
103×
103
×10
3×
103
%L
en.
×10
3×
103
×10
3×
103
%L
en.
CD
142.5
8-1
0.45
142.
2113
9.94
92.8
21.
000
101.
19-5
.35
101.
0699
.47
94.1
41.
000
MI
149.2
09.
7914
8.89
148.
6194
.38
1.06
210
4.86
5.12
104.
7410
3.52
94.5
61.
041
NM
1014
4.1
9-1
0.52
143.
8214
1.27
93.0
81.
009
102.
25-5
.30
102.
1310
0.42
93.8
61.
010
NM
2014
8.1
9-8
.79
147.
9514
5.16
93.1
21.
037
105.
29-4
.32
105.
2210
3.11
93.9
01.
037
NM
3015
3.1
3-8
.51
152.
9115
0.43
93.0
01.
075
108.
97-3
.32
108.
9410
6.92
94.0
01.
075
NM
4015
9.4
5-8
.03
159.
2615
6.75
93.2
61.
120
111.
80-4
.63
111.
7211
1.21
93.9
81.
118
NM
5016
6.6
9-8
.58
166.
4816
3.59
93.0
21.
169
117.
31-4
.40
117.
2411
6.12
94.3
01.
167
NM
6017
5.6
8-5
.11
175.
6217
1.54
92.7
21.
226
123.
15-3
.59
123.
1112
1.41
93.5
21.
221
NM
7018
1.2
5-4
.39
181.
2217
9.37
93.3
01.
282
128.
33-1
.19
128.
3412
7.11
94.3
21.
278
NM
8018
9.0
5-5
.47
188.
9918
7.09
92.6
21.
337
131.
68-3
.81
131.
6413
2.37
94.3
61.
331
NM
9019
6.3
2-7
.99
196.
1819
4.73
92.6
01.
391
139.
57-3
.26
139.
5413
8.25
93.6
01.
390
86
Tab
leE
27:
Infe
ren
cefo
rth
eva
rian
ceσ
2b
ased
onfu
lly
mas
kedN
(µ=
0,σ
2=
1)d
ata
Res
ult
sfo
rn
=10
00R
esu
lts
forn
=20
00
RM
SE
Bia
sS
DS
DC
vg.
Rel
.R
MS
EB
ias
SD
SD
Cvg.
Rel
.×
103×
103×
103×
103
%L
en.
×10
3×
103×
103×
103
%L
en.
CD
44.
56-1
.36
44.5
444
.66
94.9
81.
000
30.7
8-0
.72
30.7
831
.60
95.7
21.
000
MI
45.
570.
6745
.57
45.7
395
.04
1.02
431
.45
0.31
31.4
532
.29
95.9
21.
022
NM
10
44.
95-1
.25
44.9
445
.10
94.7
21.
010
31.0
7-0
.80
31.0
631
.90
95.6
61.
010
NM
20
46.
24-1
.33
46.2
246
.25
95.0
81.
036
32.0
6-0
.59
32.0
632
.73
95.6
41.
036
NM
30
47.
67-1
.32
47.6
647
.91
95.1
41.
073
33.2
8-0
.83
33.2
833
.89
95.5
81.
073
NM
40
49.
71-0
.99
49.7
149
.90
95.1
21.
117
34.9
2-0
.55
34.9
235
.30
95.7
21.
117
NM
50
51.
74-0
.98
51.7
452
.09
94.9
61.
166
36.3
0-0
.99
36.2
936
.83
94.7
21.
165
NM
60
54.
06-1
.67
54.0
454
.37
94.5
81.
217
37.4
2-0
.22
37.4
238
.50
95.7
41.
218
NM
70
56.
55-1
.53
56.5
356
.79
94.9
01.
272
39.3
2-0
.64
39.3
140
.19
95.2
81.
272
NM
80
59.
01-0
.98
59.0
059
.33
95.0
81.
328
41.4
5-0
.77
41.4
541
.95
94.8
61.
328
NM
90
61.
420.
2361
.43
61.9
995
.00
1.38
842
.73
-0.6
342
.73
43.7
995
.38
1.38
6
87
Tab
leE
28:
Infe
ren
cefo
rth
e84
thp
erce
nti
leµ
+σ
bas
edon
fully
mas
kedN
(µ=
0,σ
2=
1)d
ata
Res
ult
sfo
rn
=30
Res
ult
sfo
rn
=50
RM
SE
Bia
sS
DS
DC
vg.
Rel
.R
MS
EB
ias
SD
SD
Cvg.
Rel
.×
103
×10
3×
103
×10
3%
Len
.×
103×
103
×10
3×
103
%L
en.
CD
223.
68-2
7.81
221.
9621
7.29
92.5
61.
000
171.
38-1
2.26
170.
9617
0.27
94.3
01.
000
MI
227.
99-1
0.12
227.
7922
9.90
93.8
41.
058
175.
17-1
.86
175.
1817
7.30
94.9
61.
041
NM
10224.
98-2
7.14
223.
3621
8.30
92.7
21.
005
172.
05-1
1.92
171.
6517
1.04
94.3
21.
005
NM
20227.
38-2
6.34
225.
8822
1.19
92.8
21.
018
174.
35-1
1.59
173.
9817
3.17
94.2
61.
017
NM
30231.
59-2
6.14
230.
1422
5.02
92.4
21.
036
177.
59-1
1.09
177.
2617
6.26
94.2
61.
035
NM
40236.
06-2
4.73
234.
7923
0.01
92.7
01.
059
179.
07-1
0.08
178.
8118
0.12
94.5
21.
058
NM
50238.
18-2
5.28
236.
8623
5.50
92.9
61.
084
187.
43-1
1.08
187.
1218
4.17
93.9
61.
082
NM
60245.
40-2
6.95
243.
9424
0.70
92.8
61.
108
187.
93-1
1.19
187.
6218
8.55
94.4
41.
107
NM
70254.
27-2
4.78
253.
0924
7.65
92.3
61.
140
195.
12-1
2.70
194.
7319
3.38
93.7
21.
136
NM
80260.
95-2
7.02
259.
5725
3.66
92.6
61.
167
199.
83-1
4.02
199.
3619
8.06
93.4
01.
163
NM
90260.
37-3
0.12
258.
6525
9.79
92.4
01.
196
204.
79-1
4.76
204.
2820
3.15
93.4
21.
193
88
Tab
leE
29:
Infe
ren
cefo
rth
e84
thp
erce
nti
leµ
+σ
bas
edon
fully
mas
kedN
(µ=
0,σ
2=
1)d
ata
Res
ult
sfo
rn
=10
0R
esu
lts
forn
=20
0
RM
SE
Bia
sS
DS
DC
vg.
Rel
.R
MS
EB
ias
SD
SD
Cvg.
Rel
.×
103×
103
×10
3×
103
%L
en.
×10
3×
103
×10
3×
103
%L
en.
CD
123.3
3-8
.36
123.
0612
1.52
94.0
01.
000
86.7
2-4
.31
86.6
286
.26
94.5
61.
000
MI
126.2
9-3
.80
126.
2512
5.20
94.2
21.
030
88.9
5-1
.53
88.9
488
.43
94.4
41.
025
NM
1012
4.0
1-8
.27
123.
7412
2.03
93.8
61.
004
87.1
7-4
.30
87.0
886
.63
94.5
81.
004
NM
2012
4.9
6-7
.48
124.
7512
3.56
94.2
61.
017
88.0
2-3
.85
87.9
487
.69
94.5
01.
017
NM
3012
7.6
4-7
.69
127.
4212
5.67
94.1
21.
034
89.8
3-3
.51
89.7
789
.22
94.5
81.
034
NM
4012
9.9
8-7
.60
129.
7712
8.25
94.0
21.
055
90.7
9-4
.08
90.7
190
.98
94.6
61.
055
NM
5013
3.8
6-8
.50
133.
6013
1.10
93.9
41.
079
93.2
1-4
.24
93.1
293
.04
94.4
41.
079
NM
6013
7.7
3-7
.02
137.
5713
4.46
93.9
81.
107
95.1
9-3
.83
95.1
295
.30
94.2
41.
105
NM
7013
9.6
8-7
.93
139.
4713
7.88
94.0
41.
135
98.1
0-2
.85
98.0
797
.78
94.5
61.
134
NM
8014
3.8
1-7
.87
143.
6114
1.33
93.9
41.
163
98.9
4-4
.02
98.8
710
0.16
94.9
01.
161
NM
9014
6.1
0-1
0.03
145.
7814
4.82
94.0
61.
192
102.
43-4
.55
102.
3410
2.84
94.6
01.
192
89
Tab
leE
30:
Infe
ren
cefo
rth
e84
thp
erce
nti
leµ
+σ
bas
edon
fully
mas
kedN
(µ=
0,σ
2=
1)d
ata
Res
ult
sfo
rn
=10
00R
esu
lts
forn
=20
00
RM
SE
Bia
sS
DS
DC
vg.
Rel
.R
MS
EB
ias
SD
SD
Cvg.
Rel
.×
103×
103×
103×
103
%L
en.
×10
3×
103×
103×
103
%L
en.
CD
38.
35-0
.38
38.3
638
.69
95.0
21.
000
26.6
5-0
.68
26.6
527
.37
95.6
01.
000
MI
39.
240.
2339
.24
39.5
095
.08
1.02
127
.13
-0.3
527
.13
27.9
395
.82
1.02
0N
M10
38.
53-0
.35
38.5
338
.86
95.2
01.
004
26.7
3-0
.72
26.7
227
.49
95.5
41.
004
NM
20
38.
95-0
.42
38.9
539
.32
95.0
61.
016
27.1
0-0
.62
27.1
027
.82
95.6
81.
016
NM
30
39.
80-0
.37
39.8
139
.99
94.8
21.
033
27.6
9-0
.77
27.6
828
.28
95.4
41.
033
NM
40
40.
55-0
.30
40.5
640
.81
94.7
01.
055
28.1
2-0
.72
28.1
128
.86
95.8
41.
054
NM
50
41.
26-0
.24
41.2
641
.73
95.0
61.
078
28.7
1-0
.85
28.7
029
.51
95.7
81.
078
NM
60
42.
33-0
.84
42.3
242
.71
95.0
61.
104
29.4
1-0
.51
29.4
130
.23
95.4
61.
104
NM
70
43.
28-0
.76
43.2
843
.78
95.3
61.
131
30.2
1-0
.63
30.2
030
.97
95.6
61.
131
NM
80
44.
72-0
.47
44.7
344
.91
95.0
21.
161
31.1
3-0
.74
31.1
331
.76
95.1
41.
160
NM
90
45.
25-0
.04
45.2
646
.13
95.5
21.
192
31.7
7-0
.78
31.7
732
.61
95.1
81.
191
90
Tab
leE
31:
Infe
ren
cefo
rth
e95
thp
erce
nti
leµ
+1.6
45σ
bas
edon
full
ym
aske
dN
(µ=
0,σ
2=
1)d
ata
Res
ult
sfo
rn
=30
Res
ult
sfo
rn
=50
RM
SE
Bia
sS
DS
DC
vg.
Rel
.R
MS
EB
ias
SD
SD
Cvg.
Rel
.×
103
×10
3×
103
×10
3%
Len
.×
103×
103
×10
3×
103
%L
en.
CD
282.
20-4
6.04
278.
4527
2.14
92.2
01.
000
214.
79-2
3.21
213.
5521
3.25
94.2
41.
000
MI
287.
75-1
6.64
287.
3028
7.96
93.6
01.
058
219.
67-6
.24
219.
6022
2.07
95.0
01.
041
NM
10284.
35-4
5.10
280.
7827
3.92
91.9
81.
007
215.
83-2
2.71
214.
6621
4.62
93.9
61.
006
NM
20288.
75-4
3.47
285.
4827
8.92
92.1
81.
025
220.
02-2
2.05
218.
9421
8.38
93.9
41.
024
NM
30295.
93-4
3.40
292.
7628
5.74
91.9
81.
050
225.
38-2
1.29
224.
4022
3.83
93.8
41.
050
NM
40303.
53-4
1.48
300.
7129
4.40
92.0
21.
082
228.
73-1
9.70
227.
9023
0.54
94.2
01.
081
NM
50308.
60-4
1.71
305.
8030
3.94
92.5
81.
117
241.
86-2
1.13
240.
9623
7.66
93.5
61.
114
NM
60321.
40-4
5.32
318.
2231
3.18
92.1
61.
151
243.
67-2
1.81
242.
7124
5.29
94.0
21.
150
NM
70335.
73-4
1.44
333.
1932
4.76
91.7
01.
193
255.
54-2
3.03
254.
5325
3.55
93.1
21.
189
NM
80345.
34-4
4.77
342.
4633
5.11
91.7
81.
231
264.
74-2
5.56
263.
5326
1.63
93.0
21.
227
NM
90346.
83-4
9.38
343.
3334
5.56
92.1
81.
270
271.
85-2
7.19
270.
5227
0.22
93.0
81.
267
91
Tab
leE
32:
Infe
ren
cefo
rth
e95
thp
erce
nti
leµ
+1.6
45σ
bas
edon
full
ym
aske
dN
(µ=
0,σ
2=
1)d
ata
Res
ult
sfo
rn
=10
0R
esu
lts
forn
=20
0
RM
SE
Bia
sS
DS
DC
vg.
Rel
.R
MS
EB
ias
SD
SD
Cvg.
Rel
.×
103×
103
×10
3×
103
%L
en.
×10
3×
103
×10
3×
103
%L
en.
CD
155.5
0-1
3.39
154.
9315
2.20
93.8
01.
000
109.
38-6
.87
109.
1710
8.04
94.5
61.
000
MI
159.2
9-5
.64
159.
2015
6.82
94.2
21.
030
112.
18-2
.36
112.
1711
0.76
94.6
41.
025
NM
1015
6.7
3-1
3.35
156.
1815
3.13
93.9
21.
006
110.
16-6
.86
109.
9610
8.71
94.4
21.
006
NM
2015
8.7
6-1
2.09
158.
3115
5.83
94.2
41.
024
111.
82-6
.14
111.
6611
0.59
94.6
21.
024
NM
3016
3.0
0-1
2.33
162.
5415
9.59
94.0
21.
049
114.
85-5
.54
114.
7211
3.30
94.2
81.
049
NM
4016
7.2
0-1
2.24
166.
7716
4.14
93.7
61.
078
116.
70-6
.59
116.
5311
6.45
94.6
21.
078
NM
5017
3.6
1-1
3.51
173.
1016
9.17
93.4
81.
111
120.
87-6
.78
120.
6912
0.05
94.6
01.
111
NM
6018
0.3
0-1
1.15
179.
9717
4.91
93.5
61.
149
124.
69-6
.21
124.
5512
3.96
94.5
61.
147
NM
7018
3.7
4-1
2.00
183.
3718
0.77
93.3
41.
188
128.
97-4
.56
128.
9012
8.18
94.5
21.
186
NM
8019
0.2
7-1
2.50
189.
8818
6.68
93.6
61.
227
130.
98-6
.65
130.
8313
2.29
94.7
41.
225
NM
9019
4.9
8-1
5.71
194.
3619
2.64
93.9
61.
266
137.
10-7
.17
136.
9313
6.79
94.6
21.
266
92
Tab
leE
33:
Infe
ren
cefo
rth
e95
thp
erce
nti
leµ
+1.6
45σ
bas
edon
full
ym
aske
dN
(µ=
0,σ
2=
1)d
ata
Res
ult
sfo
rn
=10
00R
esu
lts
forn
=20
00
RM
SE
Bia
sS
DS
DC
vg.
Rel
.R
MS
EB
ias
SD
SD
Cvg.
Rel
.×
103×
103×
103×
103
%L
en.
×10
3×
103×
103×
103
%L
en.
CD
48.
05-0
.98
48.0
548
.46
95.0
01.
000
33.4
3-0
.98
33.4
234
.28
95.5
41.
000
MI
49.
15-0
.03
49.1
649
.47
95.0
21.
021
34.0
3-0
.49
34.0
334
.98
95.7
21.
020
NM
10
48.
36-0
.92
48.3
548
.77
95.2
41.
006
33.5
9-1
.05
33.5
834
.50
95.4
81.
006
NM
20
49.
17-1
.02
49.1
649
.59
94.8
61.
023
34.2
8-0
.89
34.2
735
.08
95.5
61.
023
NM
30
50.
56-0
.97
50.5
550
.78
95.2
01.
048
35.2
8-1
.12
35.2
635
.92
95.2
61.
048
NM
40
51.
87-0
.82
51.8
652
.23
95.1
41.
078
36.1
9-1
.00
36.1
836
.94
95.7
01.
078
NM
50
53.
21-0
.77
53.2
153
.84
95.0
81.
111
37.2
3-1
.28
37.2
138
.07
95.7
01.
111
NM
60
55.
03-1
.61
55.0
155
.56
94.7
41.
146
38.2
5-0
.70
38.2
539
.32
95.3
81.
147
NM
70
56.
72-1
.51
56.7
057
.39
95.3
81.
184
39.6
9-0
.96
39.6
840
.60
95.7
41.
184
NM
80
59.
06-1
.06
59.0
659
.32
94.9
81.
224
41.2
6-1
.13
41.2
541
.95
95.0
01.
224
NM
90
60.
19-0
.27
60.1
961
.36
95.4
21.
266
42.2
5-1
.13
42.2
443
.37
95.7
61.
265
93
Tab
leE
34:
Infe
ren
cefo
rµ
+σ
2/2
bas
edon
full
ym
aske
dN
(µ=
0,σ
2=
1)d
ata
Res
ult
sfo
rn
=30
Res
ult
sfo
rn
=50
RM
SE
Bia
sS
DS
DC
vg.
Rel
.R
MS
EB
ias
SD
SD
Cvg.
Rel
.×
103
×10
3×
103
×10
3%
Len
.×
103×
103
×10
3×
103
%L
en.
CD
221.
49-1
9.01
220.
7021
6.90
92.6
61.
000
170.
31-7
.35
170.
1717
0.03
94.3
81.
000
MI
231.
7116
.91
231.
1223
8.29
94.6
21.
099
176.
8313
.51
176.
3318
0.82
95.5
01.
063
NM
10
222.
92-1
8.18
222.
2021
7.98
92.5
81.
005
171.
02-6
.95
170.
8917
0.83
94.4
41.
005
NM
20
225.
68-1
6.93
225.
0622
1.04
92.7
81.
019
173.
38-6
.32
173.
2817
3.02
94.4
01.
018
NM
30
229.
87-1
6.13
229.
3322
4.97
92.3
61.
037
176.
69-5
.50
176.
6317
6.18
94.4
41.
036
NM
40
234.
40-1
4.06
234.
0023
0.16
92.6
21.
061
178.
28-4
.12
178.
2518
0.16
94.5
81.
060
NM
50
236.
99-1
3.68
236.
6223
5.92
93.0
21.
088
186.
90-4
.40
186.
8618
4.30
93.8
81.
084
NM
60
244.
35-1
4.30
243.
9624
1.12
92.7
81.
112
187.
40-4
.16
187.
3818
8.69
94.6
01.
110
NM
70
253.
99-1
0.63
253.
7924
8.76
92.4
41.
147
194.
35-4
.81
194.
3119
3.74
93.7
81.
139
NM
80
260.
01-1
2.21
259.
7525
4.84
92.6
01.
175
199.
37-5
.28
199.
3219
8.46
93.5
61.
167
NM
90
259.
20-1
4.50
258.
8226
0.97
92.3
21.
203
204.
13-5
.46
204.
0820
3.56
93.3
81.
197
94
Tab
leE
35:
Infe
ren
cefo
rµ
+σ
2/2
bas
edon
full
ym
aske
dN
(µ=
0,σ
2=
1)d
ata
Res
ult
sfo
rn
=10
0R
esu
lts
forn
=20
0
RM
SE
Bia
sS
DS
DC
vg.
Rel
.R
MS
EB
ias
SD
SD
Cvg.
Rel
.×
103
×10
3×
103
×10
3%
Len
.×
103×
103
×10
3×
103
%L
en.
CD
123.
16-5
.79
123.
0312
1.48
94.0
01.
000
86.6
0-3
.02
86.5
586
.24
94.5
41.
000
MI
126.
953.
9612
6.90
126.
4594
.50
1.04
189
.15
2.30
89.1
388
.86
94.8
01.
030
NM
10123.
85-5
.64
123.
7412
1.99
93.8
41.
004
87.0
7-2
.98
87.0
386
.62
94.6
01.
004
NM
20124.
88-4
.71
124.
8112
3.57
94.2
81.
017
87.9
5-2
.46
87.9
387
.69
94.5
61.
017
NM
30127.
53-4
.74
127.
4512
5.69
94.1
21.
035
89.7
7-2
.02
89.7
689
.24
94.5
21.
035
NM
40129.
97-4
.42
129.
9112
8.30
94.1
41.
056
90.6
5-2
.51
90.6
290
.99
94.6
01.
055
NM
50133.
90-5
.03
133.
8213
1.17
93.9
21.
080
93.0
9-2
.52
93.0
793
.06
94.4
41.
079
NM
60137.
79-3
.17
137.
7713
4.66
93.8
01.
109
95.1
1-1
.93
95.1
095
.35
94.3
01.
106
NM
70139.
71-3
.83
139.
6713
8.13
93.8
41.
137
98.2
3-0
.81
98.2
497
.89
94.5
01.
135
NM
80144.
12-3
.44
144.
1014
1.59
93.8
41.
166
98.9
3-1
.85
98.9
210
0.23
94.9
21.
162
NM
90146.
08-5
.20
146.
0114
5.06
94.0
41.
194
102.
28-2
.11
102.
2710
2.94
94.7
21.
194
95
Tab
leE
36:
Infe
ren
cefo
rµ
+σ
2/2
bas
edon
full
ym
aske
dN
(µ=
0,σ
2=
1)d
ata
Res
ult
sfo
rn
=10
00R
esu
lts
forn
=20
00
RM
SE
Bia
sS
DS
DC
vg.
Rel
.R
MS
EB
ias
SD
SD
Cvg.
Rel
.×
103×
103×
103×
103
%L
en.
×10
3×
103×
103×
103
%L
en.
CD
38.
36-0
.13
38.3
638
.69
95.0
61.
000
26.6
4-0
.56
26.6
427
.37
95.6
21.
000
MI
39.
280.
9839
.27
39.5
395
.14
1.02
227
.13
0.01
27.1
327
.94
95.8
21.
021
NM
10
38.
53-0
.10
38.5
438
.86
95.2
61.
004
26.7
2-0
.60
26.7
127
.49
95.5
01.
004
NM
20
38.
96-0
.15
38.9
639
.32
95.0
81.
016
27.0
9-0
.49
27.0
927
.82
95.6
41.
016
NM
30
39.
80-0
.08
39.8
039
.98
94.7
81.
033
27.6
8-0
.63
27.6
728
.28
95.4
21.
033
NM
40
40.
560.
0140
.56
40.8
194
.74
1.05
528
.11
-0.5
728
.11
28.8
695
.84
1.05
5N
M50
41.
260.
0941
.26
41.7
395
.10
1.07
928
.70
-0.6
928
.70
29.5
195
.78
1.07
8N
M60
42.
32-0
.47
42.3
242
.71
95.1
21.
104
29.4
1-0
.34
29.4
130
.23
95.4
61.
104
NM
70
43.
26-0
.36
43.2
743
.78
95.3
21.
131
30.2
0-0
.43
30.2
030
.97
95.6
41.
132
NM
80
44.
73-0
.03
44.7
344
.92
94.9
41.
161
31.1
2-0
.52
31.1
231
.76
95.1
61.
160
NM
90
45.
260.
4445
.26
46.1
595
.44
1.19
331
.76
-0.5
631
.76
32.6
195
.18
1.19
1
96
Tab
leE
37:
Infe
ren
cefo
rth
em
ean
bas
edon
Exp
onen
tial
(mea
n=
1)d
ata
wit
hC
=2.
996
=95
thp
erce
nti
le
Res
ult
sfo
rn
=10
0R
esu
lts
forn
=20
0
RM
SE
Bia
sS
DS
DC
vg.
Rel
.R
MS
EB
ias
SD
SD
Cvg.
Rel
.×
103
×10
3×
103
×10
3%
Len
.×
103×
103×
103×
103
%L
en.
CD
99.
45-0
.65
99.4
699
.93
94.6
41.
000
70.7
1-1
.16
70.7
170
.63
94.8
61.
000
MI.
C90
104.3
6-4
.31
104.
2999
.75
93.3
20.
998
73.9
8-3
.12
73.9
270
.59
93.4
80.
999
MI.
C80
108.7
50.
9510
8.76
100.
5092
.78
1.00
676
.28
-0.6
476
.28
70.8
993
.08
1.00
4M
I.D
9076
9.4
213
7.33
757.
1416
1.17
95.2
01.
613
101.
3537
.12
94.3
276
.72
95.2
41.
086
MI.
D80
117.6
260
.71
100.
7511
1.41
96.1
41.
115
76.8
326
.35
72.1
875
.19
95.7
01.
065
CE
NS
102.4
70.
6710
2.47
102.
5595
.36
1.02
672
.57
-0.2
272
.57
72.5
295
.04
1.02
7N
M10
.199.
54-0
.50
99.5
410
0.07
94.6
81.
001
70.8
8-1
.06
70.8
770
.72
94.6
21.
001
NM
10.2
99.
56-0
.50
99.5
710
0.08
94.6
81.
001
70.8
8-1
.08
70.8
770
.73
94.6
41.
001
NM
20.1
99.
94-0
.59
99.9
510
0.36
94.6
21.
004
71.0
7-1
.00
71.0
770
.94
94.7
21.
004
NM
20.2
99.
99-0
.54
100.
0010
0.42
94.7
01.
005
71.0
9-1
.06
71.0
970
.98
94.6
61.
005
NM
30.1
100.1
2-0
.29
100.
1310
0.75
94.6
41.
008
71.2
7-0
.85
71.2
771
.20
94.8
01.
008
NM
30.2
100.3
1-0
.10
100.
3210
0.96
94.8
01.
010
71.4
0-0
.92
71.4
071
.33
94.7
61.
010
NM
40.1
100.4
1-0
.66
100.
4210
1.02
94.6
61.
011
71.4
5-0
.72
71.4
571
.44
94.8
21.
011
NM
40.2
100.6
7-0
.77
100.
6810
1.48
94.7
61.
015
71.6
2-0
.78
71.6
271
.77
94.8
81.
016
NM
50.1
100.9
00.
1210
0.91
101.
3694
.82
1.01
471
.61
-0.6
871
.61
71.6
194
.90
1.01
4N
M50
.210
1.7
40.
5410
1.74
102.
3594
.76
1.02
472
.22
-0.8
072
.22
72.2
794
.58
1.02
3N
M60
.110
0.9
2-0
.14
100.
9310
1.50
94.5
81.
016
71.7
3-0
.74
71.7
371
.72
95.1
01.
015
NM
60.2
102.2
40.
2210
2.25
103.
1994
.66
1.03
372
.60
-0.9
272
.60
72.8
794
.86
1.03
2N
M70
.110
1.0
80.
0310
1.09
101.
6594
.68
1.01
771
.89
-0.4
671
.89
71.8
394
.68
1.01
7N
M70
.210
3.8
20.
7210
3.83
104.
3294
.68
1.04
473
.55
-0.2
873
.56
73.6
794
.94
1.04
3N
M80
.110
1.4
70.
2110
1.48
101.
7694
.74
1.01
871
.88
-0.4
771
.89
71.9
095
.10
1.01
8N
M80
.210
5.4
91.
0210
5.50
105.
6494
.80
1.05
774
.64
-0.2
074
.65
74.5
894
.80
1.05
6N
M90
.110
1.4
00.
1410
1.41
101.
8394
.62
1.01
971
.83
-0.5
571
.84
71.9
494
.88
1.01
9N
M90
.210
7.0
91.
2110
7.09
107.
1794
.68
1.07
275
.43
-0.6
575
.43
75.5
994
.70
1.07
0
97
Tab
leE
38:
Infe
ren
cefo
rth
em
ean
bas
edon
Exp
onen
tial
(mea
n=
1)d
ata
wit
hC
=2.
996
=95
thp
erce
nti
le
Res
ult
sfo
rn
=10
00R
esu
lts
forn
=20
00
RM
SE
Bia
sS
DS
DC
vg.
Rel
.R
MS
EB
ias
SD
SD
Cvg.
Rel
.×
103
×10
3×
103×
103
%L
en.
×10
3×
103×
103×
103
%L
en.
CD
31.9
5-0
.02
31.9
631
.62
94.8
61.
000
22.3
80.
4522
.37
22.3
794
.82
1.00
0M
I.C
90
33.5
1-0
.34
33.5
131
.65
93.7
01.
001
23.4
40.
3523
.44
22.3
993
.84
1.00
1M
I.C
80
34.5
90.
4134
.59
31.7
292
.84
1.00
324
.18
0.78
24.1
722
.43
93.0
01.
003
MI.
D90
33.3
06.
7232
.62
32.5
895
.04
1.03
023
.25
3.79
22.9
422
.95
94.7
01.
026
MI.
D80
33.2
35.
2932
.81
32.7
094
.88
1.03
423
.14
3.07
22.9
423
.05
94.8
81.
030
CE
NS
32.8
70.
0532
.87
32.4
494
.54
1.02
622
.96
0.63
22.9
622
.95
95.0
41.
026
NM
10.
132
.04
-0.0
232
.04
31.6
694
.76
1.00
122
.41
0.48
22.4
122
.40
95.0
21.
001
NM
10.
232
.06
-0.0
132
.06
31.6
694
.70
1.00
122
.41
0.48
22.4
122
.40
94.9
61.
001
NM
20.
132
.07
-0.0
332
.07
31.7
694
.88
1.00
422
.45
0.46
22.4
522
.47
94.9
01.
004
NM
20.
232
.07
-0.0
232
.07
31.7
794
.80
1.00
522
.46
0.44
22.4
522
.48
94.8
21.
005
NM
30.
132
.25
-0.0
832
.25
31.8
794
.80
1.00
822
.55
0.51
22.5
522
.55
95.0
81.
008
NM
30.
232
.30
-0.0
532
.30
31.9
394
.96
1.01
022
.59
0.54
22.5
922
.59
94.9
81.
010
NM
40.
132
.30
0.04
32.3
031
.97
94.9
21.
011
22.6
40.
5522
.64
22.6
294
.90
1.01
1N
M40.
232
.38
0.08
32.3
932
.12
94.9
01.
016
22.7
70.
5522
.76
22.7
294
.84
1.01
6N
M50.
132
.38
-0.0
432
.39
32.0
494
.68
1.01
322
.73
0.54
22.7
322
.67
94.9
41.
013
NM
50.
232
.72
0.08
32.7
232
.35
94.5
01.
023
23.0
20.
5823
.02
22.8
894
.54
1.02
3N
M60.
132
.52
0.01
32.5
232
.09
95.0
21.
015
22.7
40.
5122
.74
22.7
195
.04
1.01
5N
M60.
233
.11
0.04
33.1
132
.62
94.6
81.
031
23.0
90.
5023
.08
23.0
895
.18
1.03
1N
M70.
132
.46
0.02
32.4
632
.13
94.7
01.
016
22.7
80.
5122
.78
22.7
394
.96
1.01
6N
M70.
233
.26
0.18
33.2
632
.96
94.9
21.
042
23.5
20.
5123
.52
23.3
194
.74
1.04
2N
M80.
132
.56
-0.0
532
.57
32.1
694
.48
1.01
722
.74
0.61
22.7
422
.75
94.9
61.
017
NM
80.
233
.69
0.20
33.6
933
.36
94.6
21.
055
23.5
80.
7323
.57
23.6
095
.12
1.05
5N
M90.
132
.63
-0.0
132
.64
32.1
894
.64
1.01
822
.73
0.56
22.7
322
.77
95.0
41.
018
NM
90.
234
.29
0.19
34.2
933
.82
94.4
01.
070
23.8
50.
5323
.84
23.9
294
.84
1.06
9
98
Tab
leE
39:
Infe
ren
cefo
rth
em
ean
bas
edon
Exp
onen
tial
(mea
n=
1)d
ata
wit
hC
=2.
303
=90
thp
erce
nti
le
Res
ult
sfo
rn
=10
0R
esu
lts
forn
=20
0
RM
SE
Bia
sS
DS
DC
vg.
Rel
.R
MS
EB
ias
SD
SD
Cvg.
Rel
.×
103
×10
3×
103
×10
3%
Len
.×
103×
103×
103×
103
%L
en.
CD
98.3
50.
6298
.35
100.
0694
.66
1.00
070
.32
-0.1
570
.32
70.7
094
.68
1.00
0M
I.C
90
107.
681.
9510
7.67
100.
5993
.02
1.00
577
.00
0.86
77.0
070
.99
92.3
61.
004
MI.
C80
114.
3713
.20
113.
6210
2.25
92.8
21.
022
80.0
35.
2879
.86
71.6
091
.84
1.01
3M
I.D
90
121.
1159
.58
105.
4611
1.53
96.2
61.
115
77.5
927
.31
72.6
375
.28
95.6
21.
065
MI.
D80
109.
2241
.89
100.
8810
8.86
97.0
21.
088
74.7
319
.96
72.0
374
.78
95.8
01.
058
CE
NS
104.
653.
9910
4.59
105.
6195
.44
1.05
574
.66
1.57
74.6
674
.59
95.0
21.
055
NM
10.
198
.59
0.71
98.6
010
0.25
94.7
21.
002
70.4
3-0
.05
70.4
470
.84
94.7
61.
002
NM
10.
298
.59
0.69
98.6
010
0.26
94.7
01.
002
70.4
4-0
.06
70.4
570
.84
94.7
41.
002
NM
20.
198
.95
0.85
98.9
610
0.73
94.8
01.
007
70.6
3-0
.10
70.6
371
.16
94.7
01.
007
NM
20.
298
.93
0.78
98.9
310
0.78
94.8
61.
007
70.7
0-0
.09
70.7
171
.20
94.8
01.
007
NM
30.
199
.98
1.65
99.9
810
1.42
94.8
61.
014
71.2
2-0
.02
71.2
271
.60
94.6
41.
013
NM
30.
2100.
151.
6310
0.14
101.
6194
.70
1.01
571
.37
0.01
71.3
871
.74
94.7
81.
015
NM
40.
1100.
511.
4310
0.51
102.
0194
.94
1.01
971
.63
0.29
71.6
472
.05
94.7
21.
019
NM
40.
2101.
001.
4110
1.00
102.
5095
.00
1.02
471
.94
0.32
71.9
572
.40
94.9
01.
024
NM
50.
1100.
681.
7510
0.68
102.
5695
.16
1.02
572
.04
0.45
72.0
472
.42
94.7
21.
024
NM
50.
2101.
571.
6310
1.57
103.
6095
.02
1.03
572
.86
0.44
72.8
773
.17
94.7
61.
035
NM
60.
1101.
523.
0010
1.48
103.
1095
.02
1.03
072
.85
0.67
72.8
572
.72
94.3
41.
029
NM
60.
2103.
563.
1210
3.53
105.
0495
.24
1.05
074
.58
0.72
74.5
874
.08
94.3
81.
048
NM
70.
1101.
882.
4810
1.86
103.
3594
.88
1.03
372
.90
0.78
72.9
072
.93
94.7
41.
032
NM
70.
2105.
653.
2610
5.61
106.
6395
.00
1.06
675
.26
0.92
75.2
675
.20
94.7
81.
064
NM
80.
1102.
002.
5610
1.98
103.
5895
.06
1.03
573
.10
0.96
73.1
073
.10
94.5
81.
034
NM
80.
2106.
882.
6710
6.85
108.
4694
.96
1.08
476
.48
1.30
76.4
876
.56
94.7
81.
083
NM
90.
1102.
192.
7310
2.16
103.
7994
.96
1.03
773
.27
0.99
73.2
773
.23
94.4
01.
036
NM
90.
2109.
694.
7410
9.60
111.
0295
.10
1.10
978
.28
0.06
78.2
978
.06
94.5
01.
104
99
Tab
leE
40:
Infe
ren
cefo
rth
em
ean
bas
edon
Exp
onen
tial
(mea
n=
1)d
ata
wit
hC
=2.
303
=90
thp
erce
nti
le
Res
ult
sfo
rn
=10
00R
esu
lts
forn
=20
00
RM
SE
Bia
sS
DS
DC
vg.
Rel
.R
MS
EB
ias
SD
SD
Cvg.
Rel
.×
103
×10
3×
103×
103
%L
en.
×10
3×
103×
103×
103
%L
en.
CD
31.1
50.
1831
.16
31.6
395
.34
1.00
022
.26
0.11
22.2
622
.36
95.0
41.
000
MI.
C90
33.8
60.
2933
.87
31.7
193
.34
1.00
324
.23
0.07
24.2
422
.42
92.8
41.
002
MI.
C80
35.1
91.
2735
.17
31.8
592
.12
1.00
725
.02
0.67
25.0
122
.50
92.2
21.
006
MI.
D90
32.4
05.
2931
.97
32.7
095
.56
1.03
422
.98
2.61
22.8
423
.04
95.3
21.
030
MI.
D80
32.5
54.
1432
.29
32.7
295
.16
1.03
423
.04
2.16
22.9
423
.07
95.2
61.
032
CE
NS
32.9
60.
3832
.97
33.3
495
.12
1.05
423
.64
0.20
23.6
423
.57
95.0
41.
054
NM
10.
131
.19
0.21
31.1
931
.69
95.2
41.
002
22.3
20.
1222
.32
22.4
095
.04
1.00
2N
M10.
231
.20
0.20
31.2
031
.69
95.2
61.
002
22.3
20.
1322
.32
22.4
195
.04
1.00
2N
M20.
131
.42
0.31
31.4
231
.84
95.3
01.
007
22.4
40.
0822
.44
22.5
195
.06
1.00
7N
M20.
231
.45
0.34
31.4
531
.86
95.3
61.
007
22.4
40.
0822
.44
22.5
295
.04
1.00
7N
M30.
131
.51
0.34
31.5
132
.03
95.0
61.
013
22.6
20.
0622
.62
22.6
495
.04
1.01
3N
M30.
231
.59
0.39
31.5
932
.10
95.1
21.
015
22.6
10.
0722
.61
22.6
995
.30
1.01
5N
M40.
131
.82
0.26
31.8
332
.22
95.1
01.
019
22.6
70.
1322
.67
22.7
895
.10
1.01
9N
M40.
232
.05
0.29
32.0
532
.38
95.0
01.
024
22.8
00.
1022
.80
22.8
995
.08
1.02
4N
M50.
132
.01
0.29
32.0
132
.38
95.0
21.
024
22.8
50.
2622
.85
22.9
095
.20
1.02
4N
M50.
232
.49
0.37
32.4
932
.72
94.8
81.
034
23.0
30.
3123
.03
23.1
394
.90
1.03
4N
M60.
132
.18
0.21
32.1
832
.50
95.2
81.
028
22.9
00.
1222
.90
22.9
894
.86
1.02
8N
M60.
232
.91
0.30
32.9
233
.11
95.5
41.
047
23.3
10.
0823
.31
23.4
195
.22
1.04
7N
M70.
132
.06
0.27
32.0
632
.59
95.2
41.
031
23.0
40.
2023
.04
23.0
494
.64
1.03
0N
M70.
232
.99
0.51
32.9
933
.61
95.2
61.
063
23.7
80.
1623
.78
23.7
695
.30
1.06
2N
M80.
132
.18
0.18
32.1
832
.66
95.3
01.
033
23.0
60.
0923
.06
23.0
995
.02
1.03
3N
M80.
233
.81
0.18
33.8
234
.19
95.1
81.
081
24.1
50.
1424
.15
24.1
895
.02
1.08
1N
M90.
132
.22
0.16
32.2
232
.71
95.2
81.
034
23.0
50.
1123
.05
23.1
395
.16
1.03
4N
M90.
234
.33
0.14
34.3
334
.91
95.2
21.
104
24.5
00.
1124
.50
24.6
895
.22
1.10
4
100
Tab
leE
41:
Infe
ren
cefo
rth
elo
gsc
ale
mea
nµ
bas
edon
LN
(µ=
0,σ
2=
1)d
ata
wit
hC
=5.
18=
95th
per
centi
le
Res
ult
sfo
rn
=10
0R
esu
lts
forn
=20
0
RM
SE
Bia
sS
DS
DC
vg.
Rel
.R
MS
EB
ias
SD
SD
Cvg.
Rel
.×
103×
103
×10
3×
103
%L
en.
×10
3×
103×
103×
103
%L
en.
CD
97.9
1-0
.60
97.9
299
.25
95.0
01.
000
70.5
3-0
.68
70.5
370
.41
95.1
81.
000
MI.
C90
98.9
9-2
.34
98.9
899
.03
94.8
20.
998
71.2
7-1
.85
71.2
570
.30
94.9
60.
998
MI.
C80
100
.33
-0.4
210
0.34
99.4
294
.48
1.00
271
.71
-0.6
271
.71
70.4
994
.78
1.00
1M
I.D
90
98.8
0-0
.78
98.8
010
2.24
95.3
41.
030
70.5
5-0
.64
70.5
570
.60
95.2
41.
003
MI.
D80
98.1
0-0
.67
98.1
099
.85
95.0
81.
006
70.6
1-0
.68
70.6
170
.63
95.1
81.
003
CE
NS
98.5
90.
1198
.60
99.8
095
.04
1.00
670
.89
-0.3
770
.89
70.7
395
.18
1.00
5N
M10.
197.9
3-0
.58
97.9
499
.26
94.9
01.
000
70.5
4-0
.70
70.5
470
.41
95.1
61.
000
NM
10.
297.9
3-0
.58
97.9
399
.26
94.9
21.
000
70.5
4-0
.70
70.5
470
.41
95.1
61.
000
NM
20.
197.9
7-0
.57
97.9
899
.28
94.9
61.
000
70.5
4-0
.66
70.5
470
.43
95.2
61.
000
NM
20.
297.9
7-0
.58
97.9
899
.29
94.9
41.
000
70.5
5-0
.67
70.5
570
.44
95.2
41.
000
NM
30.
197.9
9-0
.49
98.0
099
.32
95.0
61.
001
70.5
6-0
.60
70.5
670
.46
95.1
61.
001
NM
30.
298.0
2-0
.50
98.0
399
.34
95.0
41.
001
70.5
8-0
.61
70.5
970
.47
95.1
21.
001
NM
40.
198.0
1-0
.44
98.0
299
.36
94.8
81.
001
70.5
9-0
.66
70.5
970
.47
95.1
41.
001
NM
40.
298.0
5-0
.46
98.0
699
.40
95.0
41.
002
70.6
0-0
.73
70.6
070
.49
95.2
01.
001
NM
50.
198.1
0-0
.39
98.1
199
.40
94.9
61.
002
70.6
4-0
.61
70.6
570
.50
95.2
21.
001
NM
50.
298.1
6-0
.38
98.1
799
.49
95.0
81.
002
70.7
2-0
.62
70.7
270
.56
95.0
41.
002
NM
60.
198.2
3-0
.41
98.2
399
.43
94.9
41.
002
70.6
5-0
.50
70.6
570
.54
95.1
41.
002
NM
60.
298.5
0-0
.45
98.5
199
.60
94.9
61.
004
70.7
6-0
.57
70.7
770
.66
94.9
61.
004
NM
70.
198.2
3-0
.30
98.2
499
.48
95.0
01.
002
70.6
9-0
.63
70.6
970
.53
95.0
61.
002
NM
70.
298.5
9-0
.46
98.6
099
.78
94.8
61.
005
70.9
1-0
.84
70.9
170
.75
95.0
61.
005
NM
80.
198.1
7-0
.37
98.1
899
.48
94.9
41.
002
70.7
8-0
.49
70.7
970
.57
95.1
61.
002
NM
80.
298.6
8-0
.52
98.6
910
0.05
94.9
21.
008
71.1
7-0
.42
71.1
770
.99
94.9
61.
008
NM
90.
198.1
8-0
.25
98.1
999
.53
95.0
41.
003
70.6
9-0
.55
70.6
970
.57
95.2
41.
002
NM
90.
299.1
1-0
.34
99.1
210
0.59
94.9
81.
013
71.1
4-0
.69
71.1
571
.32
95.4
21.
013
101
Tab
leE
42:
Infe
ren
cefo
rth
elo
gsc
ale
mea
nµ
bas
edon
LN
(µ=
0,σ
2=
1)d
ata
wit
hC
=5.
18=
95th
per
centi
le
Res
ult
sfo
rn
=10
00R
esu
lts
forn
=20
00
RM
SE
Bia
sS
DS
DC
vg.
Rel
.R
MS
EB
ias
SD
SD
Cvg.
Rel
.×
103
×10
3×
103×
103
%L
en.
×10
3×
103×
103×
103
%L
en.
CD
31.5
9-0
.43
31.5
931
.59
95.2
01.
000
22.4
6-0
.07
22.4
622
.35
94.6
41.
000
MI.
C90
31.8
1-0
.69
31.8
131
.59
95.0
01.
000
22.6
3-0
.15
22.6
322
.36
94.4
81.
000
MI.
C80
32.2
2-0
.28
32.2
231
.62
94.7
61.
001
22.7
8-0
.07
22.7
822
.37
94.5
01.
001
MI.
D90
31.6
0-0
.42
31.6
031
.61
95.1
81.
001
22.4
6-0
.06
22.4
622
.37
94.6
41.
001
MI.
D80
31.6
1-0
.44
31.6
131
.63
95.1
21.
001
22.4
6-0
.05
22.4
622
.38
94.6
41.
001
CE
NS
31.6
9-0
.38
31.6
931
.71
95.1
01.
004
22.5
20.
0222
.53
22.4
494
.64
1.00
4N
M10.
131
.59
-0.4
231
.59
31.5
995
.22
1.00
022
.46
-0.0
622
.46
22.3
694
.66
1.00
0N
M10.
231
.59
-0.4
231
.59
31.5
995
.20
1.00
022
.46
-0.0
622
.46
22.3
694
.66
1.00
0N
M20.
131
.60
-0.4
231
.60
31.6
095
.34
1.00
022
.47
-0.0
622
.47
22.3
694
.54
1.00
0N
M20.
231
.60
-0.4
231
.60
31.6
095
.26
1.00
022
.47
-0.0
622
.48
22.3
694
.54
1.00
0N
M30.
131
.59
-0.4
231
.59
31.6
195
.22
1.00
122
.47
-0.0
622
.47
22.3
794
.70
1.00
1N
M30.
231
.61
-0.4
231
.61
31.6
195
.22
1.00
122
.48
-0.0
622
.49
22.3
794
.64
1.00
1N
M40.
131
.62
-0.4
031
.62
31.6
295
.30
1.00
122
.47
-0.0
622
.47
22.3
794
.68
1.00
1N
M40.
231
.66
-0.4
031
.66
31.6
395
.48
1.00
122
.49
-0.0
622
.49
22.3
894
.60
1.00
1N
M50.
131
.60
-0.4
031
.60
31.6
395
.20
1.00
122
.48
-0.0
422
.48
22.3
894
.72
1.00
1N
M50.
231
.64
-0.4
131
.64
31.6
695
.34
1.00
222
.51
-0.0
522
.51
22.4
094
.62
1.00
2N
M60.
131
.65
-0.4
231
.65
31.6
495
.14
1.00
122
.47
-0.0
322
.47
22.3
994
.66
1.00
1N
M60.
231
.72
-0.4
431
.72
31.6
995
.20
1.00
322
.52
-0.0
122
.52
22.4
394
.58
1.00
3N
M70.
131
.64
-0.4
431
.64
31.6
495
.20
1.00
222
.50
-0.0
122
.50
22.3
994
.78
1.00
2N
M70.
231
.74
-0.4
431
.74
31.7
595
.14
1.00
522
.58
-0.0
322
.58
22.4
794
.62
1.00
5N
M80.
131
.63
-0.4
131
.63
31.6
595
.38
1.00
222
.50
-0.0
422
.50
22.4
094
.78
1.00
2N
M80.
231
.78
-0.4
431
.78
31.8
495
.22
1.00
822
.68
-0.0
322
.69
22.5
394
.76
1.00
8N
M90.
131
.61
-0.4
131
.61
31.6
595
.26
1.00
222
.50
-0.0
222
.50
22.4
094
.76
1.00
2N
M90.
231
.96
-0.4
631
.96
32.0
095
.30
1.01
322
.70
-0.0
122
.70
22.6
594
.84
1.01
3
102
Tab
leE
43:
Infe
ren
cefo
rth
elo
gsc
ale
vari
anceσ
2b
ased
onLN
(µ=
0,σ
2=
1)d
ata
wit
hC
=5.
18=
95th
per
centi
le
Res
ult
sfo
rn
=10
0R
esu
lts
forn
=20
0
RM
SE
Bia
sS
DS
DC
vg.
Rel
.R
MS
EB
ias
SD
SD
Cvg.
Rel
.×
103
×10
3×
103
×10
3%
Len
.×
103×
103
×10
3×
103
%L
en.
CD
139.8
9-1
0.04
139.
5414
0.00
93.6
21.
000
99.1
3-5
.98
98.9
699
.40
93.9
01.
000
MI.
C90
149.4
1-1
4.14
148.
7613
9.95
91.9
81.
000
105.
08-9
.13
104.
6999
.35
92.5
61.
000
MI.
C80
153.1
4-7
.06
152.
9914
1.48
91.7
41.
011
107.
75-4
.53
107.
6610
0.09
92.0
81.
007
MI.
D90
18835.
3134
6.71
1883
4.00
620.
6795
.06
4.43
310
1.57
-1.5
510
1.57
100.
5794
.22
1.01
2M
I.D
80
141.7
7-0
.38
141.
7814
2.67
94.0
21.
019
100.
13-1
.67
100.
1310
0.43
94.1
81.
010
CE
NS
146.2
4-6
.57
146.
1114
6.52
93.5
41.
047
103.
28-4
.51
103.
1910
3.72
93.8
61.
043
NM
10.1
140.0
0-9
.98
139.
6614
0.10
93.4
81.
001
99.2
4-6
.05
99.0
699
.46
93.8
21.
001
NM
10.2
140.0
0-9
.99
139.
6614
0.11
93.5
01.
001
99.2
5-6
.05
99.0
799
.46
93.8
61.
001
NM
20.1
140.1
8-9
.88
139.
8414
0.37
93.5
21.
003
99.3
5-5
.87
99.1
999
.66
94.0
01.
003
NM
20.2
140.1
8-9
.93
139.
8514
0.40
93.5
81.
003
99.4
0-5
.91
99.2
499
.68
93.9
61.
003
NM
30.1
140.8
3-9
.56
140.
5214
0.77
93.4
41.
006
99.7
1-5
.61
99.5
699
.94
93.8
81.
005
NM
30.2
140.9
7-9
.59
140.
6614
0.89
93.4
01.
006
99.8
6-5
.63
99.7
110
0.03
93.9
61.
006
NM
40.1
141.2
1-9
.30
140.
9214
1.23
93.5
81.
009
99.4
5-5
.89
99.2
910
0.21
93.9
81.
008
NM
40.2
141.6
2-9
.34
141.
3214
1.53
93.5
01.
011
99.6
6-6
.11
99.4
810
0.41
94.0
21.
010
NM
50.1
141.8
2-9
.10
141.
5414
1.69
93.5
01.
012
100.
19-5
.68
100.
0410
0.54
93.8
21.
011
NM
50.2
142.7
9-9
.09
142.
5114
2.34
93.6
01.
017
100.
78-5
.71
100.
6310
1.00
94.0
81.
016
NM
60.1
141.8
5-9
.14
141.
5714
2.08
93.3
61.
015
100.
45-5
.11
100.
3310
0.88
93.9
61.
015
NM
60.2
143.2
9-9
.29
143.
0014
3.27
93.1
41.
023
101.
38-5
.36
101.
2410
1.72
94.1
81.
023
NM
70.1
142.5
2-8
.60
142.
2814
2.52
93.6
21.
018
100.
17-5
.71
100.
0210
1.07
93.9
21.
017
NM
70.2
144.7
2-9
.12
144.
4514
4.50
93.6
01.
032
101.
71-6
.37
101.
5210
2.47
94.0
61.
031
NM
80.1
141.8
4-8
.90
141.
5714
2.79
93.8
01.
020
100.
92-5
.13
100.
8010
1.35
93.8
41.
020
NM
80.2
144.5
2-9
.35
144.
2414
5.96
93.8
81.
043
103.
38-5
.04
103.
2710
3.67
93.8
21.
043
NM
90.1
142.4
5-8
.36
142.
2214
3.12
93.7
01.
022
100.
83-5
.38
100.
7010
1.49
93.9
61.
021
NM
90.2
147.4
6-8
.60
147.
2314
7.79
93.8
41.
056
104.
36-5
.85
104.
2110
4.81
94.2
41.
054
103
Tab
leE
44:
Infe
ren
cefo
rth
elo
gsc
ale
vari
anceσ
2b
ased
onLN
(µ=
0,σ
2=
1)d
ata
wit
hC
=5.
18=
95th
per
centi
le
Res
ult
sfo
rn
=10
00R
esu
lts
forn
=20
00
RM
SE
Bia
sS
DS
DC
vg.
Rel
.R
MS
EB
ias
SD
SD
Cvg.
Rel
.×
103
×10
3×
103×
103
%L
en.
×10
3×
103×
103×
103
%L
en.
CD
45.2
8-1
.43
45.2
644
.66
94.1
81.
000
31.6
8-0
.28
31.6
931
.61
95.1
41.
000
MI.
C90
48.1
9-2
.18
48.1
444
.71
92.6
81.
001
33.4
6-0
.42
33.4
631
.67
93.5
01.
002
MI.
C80
49.0
9-0
.83
49.0
944
.85
92.3
01.
004
34.3
7-0
.05
34.3
831
.74
92.6
81.
004
MI.
D90
45.3
8-0
.76
45.3
844
.80
94.4
21.
003
31.7
40.
0731
.75
31.7
095
.20
1.00
3M
I.D
80
45.4
1-0
.66
45.4
144
.87
94.4
01.
005
31.8
90.
1431
.90
31.7
595
.14
1.00
4C
EN
S47
.11
-1.2
247
.10
46.5
094
.60
1.04
132
.75
0.11
32.7
532
.92
95.2
41.
041
NM
10.
145
.34
-1.4
245
.32
44.6
994
.22
1.00
131
.72
-0.2
631
.72
31.6
495
.14
1.00
1N
M10.
245
.35
-1.4
245
.33
44.6
994
.24
1.00
131
.72
-0.2
631
.72
31.6
495
.16
1.00
1N
M20.
145
.41
-1.4
245
.39
44.7
794
.18
1.00
331
.77
-0.2
431
.77
31.6
995
.20
1.00
3N
M20.
245
.43
-1.4
245
.42
44.7
894
.08
1.00
331
.77
-0.2
531
.77
31.7
095
.18
1.00
3N
M30.
145
.48
-1.4
345
.47
44.8
994
.36
1.00
531
.82
-0.2
531
.82
31.7
895
.12
1.00
5N
M30.
245
.55
-1.4
245
.54
44.9
294
.34
1.00
631
.84
-0.2
431
.85
31.8
095
.12
1.00
6N
M40.
145
.68
-1.3
245
.67
45.0
294
.08
1.00
831
.91
-0.2
331
.91
31.8
795
.22
1.00
8N
M40.
245
.75
-1.3
245
.74
45.1
294
.06
1.01
031
.99
-0.2
431
.99
31.9
495
.06
1.01
0N
M50.
145
.84
-1.3
245
.83
45.1
694
.30
1.01
131
.95
-0.1
431
.96
31.9
795
.00
1.01
1N
M50.
246
.07
-1.3
646
.06
45.3
794
.34
1.01
632
.19
-0.1
732
.19
32.1
294
.82
1.01
6N
M60.
145
.97
-1.4
145
.95
45.2
894
.12
1.01
431
.94
-0.1
331
.95
32.0
695
.20
1.01
4N
M60.
246
.36
-1.4
946
.34
45.6
794
.22
1.02
332
.17
-0.0
532
.18
32.3
495
.08
1.02
3N
M70.
145
.92
-1.5
645
.89
45.3
994
.22
1.01
632
.13
-0.0
232
.14
32.1
495
.10
1.01
7N
M70.
246
.59
-1.5
446
.57
46.0
594
.32
1.03
132
.66
-0.0
632
.66
32.6
195
.20
1.03
2N
M80.
146
.15
-1.3
546
.13
45.4
994
.42
1.01
932
.36
-0.1
332
.36
32.2
194
.86
1.01
9N
M80.
247
.20
-1.4
247
.19
46.5
494
.12
1.04
233
.25
-0.1
333
.25
32.9
594
.72
1.04
2N
M90.
146
.02
-1.3
746
.01
45.5
794
.50
1.02
032
.22
-0.0
632
.23
32.2
695
.12
1.02
0N
M90.
247
.59
-1.5
547
.57
47.0
994
.14
1.05
433
.38
-0.0
433
.38
33.3
594
.98
1.05
5
104
Tab
leE
45:
Infe
ren
cefo
rth
em
eaneµ
+σ2/2
bas
edon
LN
(µ=
0,σ
2=
1)d
ata
wit
hC
=5.
18=
95th
per
centi
le
Res
ult
sfo
rn
=10
0R
esu
lts
forn
=20
0
RM
SE
Bia
sS
DS
DC
vg.
Rel
.R
MS
EB
ias
SD
SD
Cvg.
Rel
.×
103
×103
×10
3×
103
%L
en.
×10
3×
103
×10
3×
103
%L
en.
CD
199
.62
2.6
419
9.62
201.
9993
.52
1.00
014
1.26
-0.0
414
1.28
142.
5994
.68
1.00
0M
I.C
90
212
.68
-0.3
321
2.70
202.
8892
.60
1.00
414
8.84
-3.0
814
8.82
142.
6893
.68
1.00
1M
I.C
80
223
.29
12.1
022
2.98
207.
4192
.50
1.02
715
3.52
4.16
153.
4814
4.50
93.3
21.
013
MI.
D90
2×
1015
3×
1013
2×
1015
9×
1014
95.0
06×
1012
MI.
D80
230
.21
18.0
122
9.53
219.
2694
.36
1.08
614
3.77
6.05
143.
6614
5.09
95.0
61.
018
CE
NS
209
.04
7.6
420
8.92
209.
5493
.98
1.03
714
6.38
2.09
146.
3814
7.15
94.6
61.
032
NM
10.1
199
.80
2.7
419
9.80
202.
1293
.60
1.00
114
1.38
-0.1
114
1.40
142.
6594
.62
1.00
0N
M10
.2199
.77
2.7
219
9.78
202.
1293
.60
1.00
114
1.39
-0.1
114
1.41
142.
6594
.68
1.00
0N
M20
.1200
.13
2.8
820
0.13
202.
4193
.58
1.00
214
1.49
0.11
141.
5014
2.87
94.7
21.
002
NM
20.2
200
.14
2.8
220
0.14
202.
4493
.72
1.00
214
1.56
0.08
141.
5714
2.89
94.9
01.
002
NM
30.1
200
.74
3.3
320
0.74
202.
9093
.64
1.00
514
1.89
0.45
141.
9114
3.19
94.7
01.
004
NM
30.2
200
.95
3.3
220
0.95
203.
0593
.66
1.00
514
2.10
0.45
142.
1214
3.30
94.6
21.
005
NM
40.1
201
.39
3.6
820
1.38
203.
4393
.78
1.00
714
1.80
0.11
141.
8114
3.43
94.9
41.
006
NM
40.2
201
.81
3.6
820
1.79
203.
8293
.72
1.00
914
1.96
-0.1
714
1.97
143.
6694
.74
1.00
8N
M50
.1202
.30
4.0
320
2.28
203.
9693
.58
1.01
014
2.63
0.44
142.
6414
3.80
94.6
41.
008
NM
50.2
203
.36
4.1
720
3.34
204.
8493
.86
1.01
414
3.38
0.46
143.
3914
4.40
94.5
21.
013
NM
60.1
202
.98
4.0
420
2.96
204.
3893
.70
1.01
214
2.90
1.11
142.
9114
4.20
94.8
81.
011
NM
60.2
204
.99
4.1
020
4.97
206.
0293
.54
1.02
014
4.02
0.88
144.
0314
5.29
94.7
21.
019
NM
70.1
203
.55
4.7
220
3.52
204.
9393
.88
1.01
514
2.89
0.40
142.
9114
4.33
94.7
81.
012
NM
70.2
206
.80
4.4
220
6.78
207.
6993
.98
1.02
814
4.93
-0.3
214
4.95
146.
1994
.56
1.02
5N
M80
.1202
.86
4.2
820
2.84
205.
1493
.92
1.01
614
3.96
1.19
143.
9714
4.69
94.6
81.
015
NM
80.2
206
.98
4.1
420
6.96
209.
7793
.84
1.03
914
7.32
1.67
147.
3214
8.04
94.6
21.
038
NM
90.1
203
.19
4.9
820
3.14
205.
5893
.84
1.01
814
3.37
0.85
143.
3814
4.80
94.7
81.
015
NM
90.2
210
.88
5.5
221
0.83
213.
1494
.10
1.05
514
8.01
0.63
148.
0314
9.96
94.7
61.
052
105
Tab
leE
46:
Infe
ren
cefo
rth
em
eaneµ
+σ2/2
bas
edon
LN
(µ=
0,σ
2=
1)d
ata
wit
hC
=5.
18=
95th
per
centi
le
Res
ult
sfo
rn
=10
00R
esu
lts
forn
=20
00
RM
SE
Bia
sS
DS
DC
vg.
Rel
.R
MS
EB
ias
SD
SD
Cvg.
Rel
.×
103
×10
3×
103×
103
%L
en.
×10
3×
103×
103×
103
%L
en.
CD
63.7
9-0
.65
63.7
963
.80
94.8
81.
000
45.1
40.
2845
.14
45.1
695
.22
1.00
0M
I.C
90
66.8
2-1
.43
66.8
163
.86
93.8
21.
001
47.0
80.
1547
.08
45.2
393
.86
1.00
1M
I.C
80
68.9
60.
6468
.96
64.1
493
.56
1.00
548
.35
0.73
48.3
545
.34
93.4
61.
004
MI.
D90
63.9
80.
1363
.98
64.0
295
.00
1.00
345
.22
0.68
45.2
245
.28
95.3
01.
003
MI.
D80
64.0
50.
4064
.06
64.1
895
.24
1.00
645
.34
0.85
45.3
445
.37
95.3
61.
005
CE
NS
65.5
6-0
.33
65.5
765
.62
95.0
21.
028
46.1
90.
7646
.19
46.4
595
.48
1.02
9N
M10.
163
.83
-0.6
363
.84
63.8
494
.78
1.00
145
.16
0.30
45.1
645
.19
95.2
21.
001
NM
10.
263
.84
-0.6
363
.85
63.8
494
.82
1.00
145
.16
0.30
45.1
745
.19
95.1
81.
001
NM
20.
163
.92
-0.6
363
.93
63.9
294
.96
1.00
245
.27
0.33
45.2
745
.25
95.1
21.
002
NM
20.
263
.96
-0.6
363
.96
63.9
394
.96
1.00
245
.28
0.32
45.2
845
.26
95.2
01.
002
NM
30.
163
.96
-0.6
463
.96
64.0
394
.94
1.00
445
.27
0.32
45.2
845
.33
95.1
21.
004
NM
30.
264
.08
-0.6
264
.08
64.0
895
.02
1.00
445
.36
0.32
45.3
645
.36
95.1
61.
004
NM
40.
164
.23
-0.5
064
.23
64.1
894
.82
1.00
645
.34
0.34
45.3
545
.42
95.2
81.
006
NM
40.
264
.41
-0.4
864
.41
64.3
094
.78
1.00
845
.46
0.32
45.4
745
.51
95.1
41.
008
NM
50.
164
.25
-0.5
064
.25
64.3
194
.80
1.00
845
.42
0.44
45.4
245
.52
95.2
81.
008
NM
50.
264
.58
-0.5
464
.58
64.5
795
.10
1.01
245
.73
0.41
45.7
345
.71
95.2
21.
012
NM
60.
164
.56
-0.5
964
.56
64.4
394
.78
1.01
045
.38
0.47
45.3
945
.61
95.2
61.
010
NM
60.
265
.13
-0.6
765
.14
64.9
394
.98
1.01
845
.75
0.57
45.7
545
.98
95.2
41.
018
NM
70.
164
.46
-0.7
664
.46
64.5
394
.92
1.01
145
.65
0.60
45.6
545
.70
95.4
41.
012
NM
70.
265
.34
-0.7
065
.34
65.4
294
.94
1.02
546
.35
0.55
46.3
546
.32
95.0
01.
026
NM
80.
164
.61
-0.5
264
.62
64.6
394
.88
1.01
345
.82
0.47
45.8
245
.75
95.1
01.
013
NM
80.
266
.02
-0.5
766
.02
66.1
095
.20
1.03
647
.12
0.51
47.1
246
.79
95.0
21.
036
NM
90.
164
.45
-0.5
564
.46
64.7
194
.86
1.01
445
.71
0.55
45.7
145
.81
95.2
81.
014
NM
90.
266
.79
-0.6
966
.80
67.0
295
.10
1.05
047
.30
0.63
47.3
047
.46
95.3
61.
051
106
Tab
leE
47:
Infe
ren
cefo
rth
eva
rian
cee2µ
+2σ2−e2µ
+σ2
bas
edon
LN
(µ=
0,σ
2=
1)d
ata
wit
hC
=5.
18=
95th
per
centi
le
Res
ult
sfo
rn
=10
0R
esu
lts
forn
=20
0
RM
SE
Bia
sS
DS
DC
vg.
Rel
.R
MS
EB
ias
SD
SD
Cvg.
Rel
.×
103
×10
3×
103
×10
3%
Len
.×
103
×10
3×
103
×10
3%
Len
.
CD
2169.1
4235
.84
2156
.49
2095
.21
89.6
81.
000
1432
.47
98.9
814
29.1
914
20.8
492
.00
1.00
0M
I.C
90
2540.5
4336
.20
2518
.44
2255
.95
87.7
81.
077
1578
.45
117.
0715
74.2
614
56.2
990
.86
1.02
5M
I.C
80
2898.6
5611
.67
2833
.66
2541
.08
89.0
21.
213
1693
.70
248.
0516
75.6
115
36.7
391
.24
1.08
2M
I.D
90
5×
1063
7×
1061
5×
1063
8×
1063
93.2
46×
1060
MI.
D80
5×
109
7×
107
5×
109
2×
109
92.2
08×
105
1555
.37
261.
4315
33.4
015
47.2
793
.50
1.08
9C
EN
S24
22.4
4335
.13
2399
.39
2261
.60
89.6
61.
079
1543
.33
139.
5015
37.1
715
03.8
692
.08
1.05
8N
M10.
121
73.3
5237
.68
2160
.53
2097
.81
89.6
41.
001
1435
.22
98.4
914
31.9
814
21.7
692
.14
1.00
1N
M10.
221
72.6
5237
.46
2159
.85
2097
.75
89.6
41.
001
1435
.38
98.5
514
32.1
314
21.8
292
.16
1.00
1N
M20.
121
79.6
1240
.46
2166
.52
2103
.56
89.8
81.
004
1437
.48
101.
4714
34.0
314
25.6
692
.16
1.00
3N
M20.
221
78.2
8239
.79
2165
.25
2103
.76
89.7
01.
004
1438
.16
101.
2014
34.7
414
25.9
692
.22
1.00
4N
M30.
121
96.7
1248
.98
2182
.78
2114
.49
89.6
41.
009
1446
.89
106.
7914
43.0
914
31.7
292
.22
1.00
8N
M30.
221
97.2
4249
.41
2183
.26
2116
.83
89.6
21.
010
1450
.00
107.
3114
46.1
714
33.3
892
.10
1.00
9N
M40.
122
21.4
2256
.10
2206
.83
2125
.67
89.7
01.
015
1443
.16
102.
1814
39.6
814
34.6
192
.36
1.01
0N
M40.
222
23.0
5257
.53
2208
.30
2131
.94
89.5
01.
018
1444
.62
99.4
714
41.3
414
37.3
892
.32
1.01
2N
M50.
122
34.0
4263
.15
2218
.71
2137
.06
89.5
01.
020
1462
.05
108.
5114
58.1
614
41.9
892
.28
1.01
5N
M50.
222
48.2
9268
.95
2232
.36
2152
.16
89.4
41.
027
1473
.97
110.
7014
69.9
514
50.8
192
.14
1.02
1N
M60.
122
47.4
0264
.79
2231
.97
2145
.14
89.6
01.
024
1465
.97
117.
4214
61.4
014
49.7
992
.42
1.02
0N
M60.
222
73.7
0272
.38
2257
.56
2171
.73
89.3
01.
037
1479
.14
117.
6014
74.6
114
64.9
192
.16
1.03
1N
M70.
122
64.3
2276
.41
2247
.61
2158
.25
89.5
81.
030
1464
.57
108.
4414
60.6
914
50.4
292
.22
1.02
1N
M70.
223
19.4
8284
.75
2302
.16
2202
.15
89.6
41.
051
1495
.50
105.
6514
91.9
114
75.5
392
.24
1.03
8N
M80.
122
49.0
1267
.85
2233
.23
2158
.77
89.7
01.
030
1486
.13
120.
6714
81.3
714
58.7
292
.06
1.02
7N
M80.
223
21.5
3280
.43
2304
.76
2228
.80
89.6
01.
064
1530
.57
133.
8415
24.8
615
05.9
592
.04
1.06
0N
M90.
122
63.3
8279
.01
2246
.34
2169
.82
89.3
81.
036
1475
.12
115.
5214
70.7
414
59.4
792
.26
1.02
7N
M90.
224
08.4
9313
.34
2388
.26
2286
.69
89.4
81.
091
1543
.02
124.
9015
38.1
115
27.5
091
.94
1.07
5
107
Tab
leE
48:
Infe
ren
cefo
rth
eva
rian
cee2µ
+2σ2−e2µ
+σ2
bas
edon
LN
(µ=
0,σ
2=
1)d
ata
wit
hC
=5.
18=
95th
per
centi
le)
Res
ult
sfo
rn
=10
00R
esu
lts
forn
=20
00
RM
SE
Bia
sS
DS
DC
vg.
Rel
.R
MS
EB
ias
SD
SD
Cvg.
Rel
.×
10
3×
103
×10
3×
103
%L
en.
×10
3×
103
×10
3×
103
%L
en.
CD
624
.10
15.2
562
3.97
618.
3894
.00
1.00
043
7.12
14.1
143
6.94
436.
7594
.88
1.00
0M
I.C
90
671
.08
15.8
567
0.96
621.
4892
.68
1.00
546
4.59
17.2
446
4.31
438.
5493
.20
1.00
4M
I.C
80
697
.96
46.8
669
6.46
629.
7292
.06
1.01
848
2.56
27.8
348
1.80
441.
3492
.50
1.01
1M
I.D
90
630
.13
32.9
262
9.33
625.
0694
.44
1.01
143
9.55
22.8
543
9.00
439.
5994
.80
1.00
7M
I.D
80
633
.04
41.6
663
1.73
629.
4394
.38
1.01
844
2.51
27.6
544
1.68
441.
5994
.88
1.01
1C
EN
S652
.93
21.5
365
2.64
646.
3194
.00
1.04
545
3.60
20.8
645
3.17
456.
3394
.96
1.04
5N
M10.
1625
.18
15.5
462
5.05
618.
8994
.00
1.00
143
7.54
14.3
043
7.35
437.
0994
.80
1.00
1N
M10.
2625
.34
15.6
562
5.21
618.
9294
.00
1.00
143
7.56
14.3
143
7.36
437.
1194
.82
1.00
1N
M20.
1626
.26
15.6
662
6.13
620.
1194
.06
1.00
343
8.75
14.7
943
8.54
437.
9994
.72
1.00
3N
M20.
2626
.64
15.7
362
6.51
620.
2993
.98
1.00
343
8.80
14.6
643
8.60
438.
1094
.74
1.00
3N
M30.
1627
.03
15.6
862
6.90
621.
8394
.04
1.00
643
9.25
14.7
043
9.05
439.
1994
.78
1.00
6N
M30.
2628
.44
15.9
662
8.30
622.
5094
.06
1.00
744
0.03
14.7
843
9.82
439.
6494
.76
1.00
7N
M40.
1630
.79
17.5
763
0.61
624.
1094
.08
1.00
944
0.39
15.0
144
0.18
440.
6194
.88
1.00
9N
M40.
2632
.66
17.9
363
2.47
625.
7893
.88
1.01
244
1.81
14.9
244
1.60
441.
7494
.68
1.01
1N
M50.
1632
.28
17.7
563
2.10
626.
1394
.24
1.01
344
1.45
16.3
144
1.19
442.
1694
.86
1.01
2N
M50.
2636
.28
17.6
363
6.10
629.
5694
.02
1.01
844
5.42
16.2
244
5.17
444.
5994
.60
1.01
8N
M60.
1636
.10
16.9
463
5.94
627.
8794
.14
1.01
544
1.08
16.5
444
0.81
443.
5094
.94
1.01
5N
M60.
2643
.58
16.6
664
3.43
634.
3393
.96
1.02
644
5.45
18.0
244
5.13
448.
2595
.00
1.02
6N
M70.
1634
.03
14.7
463
3.92
629.
1594
.26
1.01
744
4.78
18.3
144
4.44
444.
8594
.80
1.01
9N
M70.
2645
.71
16.3
964
5.56
640.
6494
.16
1.03
645
3.63
18.3
945
3.30
452.
7794
.70
1.03
7N
M80.
1638
.29
17.9
563
8.10
631.
0494
.02
1.02
044
7.69
16.9
844
7.41
445.
6694
.84
1.02
0N
M80.
2657
.02
19.0
865
6.81
649.
3993
.90
1.05
046
3.34
18.4
446
3.02
458.
6394
.48
1.05
0N
M90.
1635
.55
17.4
163
5.38
632.
0593
.94
1.02
244
5.44
17.8
044
5.13
446.
5294
.76
1.02
2N
M90.
2663
.99
18.2
766
3.80
659.
7894
.18
1.06
746
5.53
19.9
146
5.15
466.
2394
.64
1.06
8
108
Tab
leE
49:
Infe
ren
cefo
rth
e84
thp
erce
nti
leeµ
+σ
bas
edon
LN
(µ=
0,σ
2=
1)d
ata
wit
hC
=5.
18=
95th
per
centi
le
Res
ult
sfo
rn
=10
0R
esu
lts
forn
=20
0
RM
SE
Bia
sS
DS
DC
vg.
Rel
.R
MS
EB
ias
SD
SD
Cvg.
Rel
.×
103
×10
3×
103
×10
3%
Len
.×
103×
103
×10
3×
103
%L
en.
CD
327.7
9-2
.39
327.
8133
1.76
93.4
81.
000
232.
57-3
.43
232.
5723
4.68
94.6
81.
000
MI.
C90
347.9
0-9
.67
347.
8033
2.28
92.4
01.
002
244.
73-9
.48
244.
5723
4.62
93.6
01.
000
MI.
C80
363.2
58.
9236
3.17
338.
1992
.26
1.01
925
1.81
1.59
251.
8323
7.10
93.2
61.
010
MI.
D90
2×
1095
3×
1093
2×
1095
7×
1095
95.2
22×
1093
867.
0515
.49
867.
0030
0.80
95.0
01.
282
MI.
D80
335.5
316
.89
335.
1434
1.46
94.2
21.
029
235.
795.
1323
5.76
238.
0194
.88
1.01
4C
EN
S34
2.0
55.
1934
2.04
343.
4994
.04
1.03
524
0.56
-0.2
124
0.58
241.
9994
.62
1.03
1N
M10.
132
8.0
7-2
.24
328.
0933
1.96
93.4
81.
001
232.
75-3
.55
232.
7523
4.78
94.6
01.
000
NM
10.
232
8.0
3-2
.26
328.
0533
1.96
93.4
81.
001
232.
77-3
.55
232.
7723
4.79
94.6
21.
000
NM
20.
132
8.5
9-2
.03
328.
6133
2.43
93.6
41.
002
232.
92-3
.19
232.
9223
5.14
94.7
41.
002
NM
20.
232
8.6
0-2
.12
328.
6333
2.48
93.6
81.
002
233.
04-3
.25
233.
0423
5.18
94.8
41.
002
NM
30.
132
9.4
9-1
.35
329.
5233
3.19
93.6
41.
004
233.
54-2
.66
233.
5523
5.65
94.5
41.
004
NM
30.
232
9.8
6-1
.38
329.
8933
3.44
93.6
01.
005
233.
89-2
.67
233.
9023
5.82
94.5
81.
005
NM
40.
133
0.4
4-0
.81
330.
4733
4.01
93.8
61.
007
233.
40-3
.19
233.
4023
6.06
94.9
21.
006
NM
40.
233
1.1
8-0
.85
331.
2133
4.66
93.6
41.
009
233.
68-3
.68
233.
6723
6.45
94.7
81.
008
NM
50.
133
1.9
1-0
.29
331.
9533
4.85
93.6
61.
009
234.
70-2
.71
234.
7123
6.63
94.5
41.
008
NM
50.
233
3.6
6-0
.16
333.
6933
6.28
93.8
81.
014
235.
92-2
.72
235.
9323
7.62
94.4
41.
012
NM
60.
133
2.9
9-0
.29
333.
0333
5.53
93.5
81.
011
235.
13-1
.62
235.
1523
7.27
94.8
61.
011
NM
60.
233
6.3
2-0
.32
336.
3533
8.18
93.5
01.
019
237.
02-2
.05
237.
0323
9.07
94.6
81.
019
NM
70.
133
3.8
10.
7833
3.84
336.
3793
.74
1.01
423
5.13
-2.7
723
5.14
237.
5094
.64
1.01
2N
M70.
233
9.0
40.
0533
9.08
340.
8793
.90
1.02
723
8.47
-4.0
723
8.46
240.
5894
.50
1.02
5N
M80.
133
2.7
50.
1133
2.78
336.
7393
.78
1.01
523
6.79
-1.5
223
6.81
238.
0594
.64
1.01
4N
M80.
233
9.4
3-0
.39
339.
4634
4.29
93.9
01.
038
242.
35-0
.91
242.
3724
3.53
94.5
01.
038
NM
90.
133
3.1
61.
2033
3.19
337.
4093
.86
1.01
723
5.89
-2.0
723
5.90
238.
2494
.78
1.01
5N
M90.
234
5.5
01.
5834
5.53
349.
6394
.12
1.05
424
3.52
-2.7
024
3.53
246.
7094
.68
1.05
1
109
Tab
leE
50:
Infe
ren
cefo
rth
e84
thp
erce
nti
leeµ
+σ
bas
edon
LN
(µ=
0,σ
2=
1)d
ata
wit
hC
=5.
18=
95th
per
centi
le
Res
ult
sfo
rn
=10
00R
esu
lts
forn
=20
00
RM
SE
Bia
sS
DS
DC
vg.
Rel
.R
MS
EB
ias
SD
SD
Cvg.
Rel
.×
103×
103
×10
3×
103
%L
en.
×10
3×
103×
103×
103
%L
en.
CD
105
.15
-1.7
710
5.14
105.
1694
.88
1.00
074
.40
0.12
74.4
174
.45
95.2
01.
000
MI.
C90
110
.11
-3.2
611
0.07
105.
2493
.86
1.00
177
.61
-0.1
877
.61
74.5
493
.88
1.00
1M
I.C
80
113
.57
-0.0
111
3.58
105.
6593
.52
1.00
579
.67
0.68
79.6
874
.71
93.4
61.
004
MI.
D90
105
.41
-0.6
410
5.42
105.
4894
.92
1.00
374
.52
0.70
74.5
374
.62
95.3
01.
002
MI.
D80
105
.52
-0.2
910
5.53
105.
7295
.12
1.00
574
.72
0.94
74.7
274
.77
95.3
61.
004
CE
NS
108
.04
-1.3
010
8.04
108.
1495
.00
1.02
876
.13
0.89
76.1
376
.56
95.4
61.
028
NM
10.
1105
.22
-1.7
410
5.21
105.
2194
.78
1.00
174
.44
0.14
74.4
574
.48
95.1
61.
001
NM
10.
2105
.23
-1.7
310
5.23
105.
2294
.80
1.00
174
.45
0.15
74.4
574
.48
95.2
21.
001
NM
20.
1105
.37
-1.7
510
5.37
105.
3594
.98
1.00
274
.61
0.20
74.6
274
.58
95.1
21.
002
NM
20.
2105
.42
-1.7
410
5.42
105.
3795
.06
1.00
274
.63
0.18
74.6
474
.60
95.1
81.
002
NM
30.
1105
.43
-1.7
510
5.42
105.
5494
.96
1.00
474
.62
0.18
74.6
374
.72
95.1
61.
004
NM
30.
2105
.62
-1.7
310
5.62
105.
6294
.98
1.00
474
.76
0.19
74.7
774
.77
95.1
41.
004
NM
40.
1105
.86
-1.5
410
5.86
105.
7794
.78
1.00
674
.74
0.21
74.7
574
.87
95.3
21.
006
NM
40.
2106
.16
-1.5
010
6.16
105.
9894
.82
1.00
874
.94
0.18
74.9
575
.01
95.1
41.
008
NM
50.
1105
.90
-1.5
410
5.90
105.
9994
.80
1.00
874
.87
0.39
74.8
775
.03
95.3
01.
008
NM
50.
2106
.44
-1.6
210
6.44
106.
4395
.08
1.01
275
.37
0.33
75.3
875
.34
95.1
41.
012
NM
60.
1106
.40
-1.6
910
6.40
106.
1994
.80
1.01
074
.81
0.42
74.8
175
.18
95.2
61.
010
NM
60.
2107
.34
-1.8
310
7.33
107.
0194
.96
1.01
875
.41
0.59
75.4
275
.78
95.2
41.
018
NM
70.
1106
.25
-1.9
710
6.24
106.
3594
.98
1.01
175
.24
0.63
75.2
575
.32
95.4
41.
012
NM
70.
2107
.70
-1.9
010
7.70
107.
8194
.92
1.02
576
.39
0.55
76.4
076
.35
95.0
41.
026
NM
80.
1106
.48
-1.5
910
6.48
106.
5294
.84
1.01
375
.52
0.41
75.5
275
.41
95.0
81.
013
NM
80.
2108
.79
-1.7
010
8.79
108.
9395
.10
1.03
677
.67
0.47
77.6
877
.13
95.0
61.
036
NM
90.
1106
.23
-1.6
210
6.23
106.
6494
.84
1.01
475
.34
0.56
75.3
475
.51
95.2
81.
014
NM
90.
2110
.09
-1.9
011
0.08
110.
4595
.10
1.05
077
.97
0.66
77.9
778
.22
95.3
61.
051
110
Tab
leE
51:
Infe
ren
cefo
rth
e95
thp
erce
nti
leeµ
+1.6
45σ
bas
edon
LN
(µ=
0,σ
2=
1)d
ata
wit
hC
=5.
18=
95th
per
centi
le
Res
ult
sfo
rn
=10
0R
esu
lts
forn
=20
0
RM
SE
Bia
sS
DS
DC
vg.
Rel
.R
MS
EB
ias
SD
SD
Cvg.
Rel
.×
103
×10
3×
103
×10
3%
Len
.×
103
×10
3×
103
×10
3%
Len
.
CD
787.
63-7
.93
787.
6779
3.99
93.1
41.
000
555.
13-9
.97
555.
1056
0.75
94.3
41.
000
MI.
C90
851.
74-2
0.91
851.
5779
8.26
91.6
81.
005
592.
52-2
3.34
592.
1256
1.40
92.8
01.
001
MI.
C80
896.
6233.4
289
6.08
818.
2291
.52
1.03
161
3.95
8.56
613.
9556
9.51
92.8
41.
016
MI.
D90
2205
24.6
031
32.4
722
0524
.41
2146
7.98
94.7
838
.284
MI.
D80
820.
2858.7
181
8.26
831.
9693
.92
1.04
856
6.91
18.9
456
6.65
572.
1094
.64
1.02
0C
EN
S833.
3814.5
583
3.34
832.
0393
.24
1.04
858
0.85
-0.4
258
0.91
584.
2994
.36
1.04
2N
M10.1
788.
48-7
.49
788.
5279
4.61
93.2
01.
001
555.
76-1
0.31
555.
7256
1.07
94.2
21.
001
NM
10.2
788.
39-7
.56
788.
4379
4.62
93.2
41.
001
555.
82-1
0.30
555.
7856
1.08
94.2
01.
001
NM
20.1
790.
00-6
.87
790.
0579
6.13
93.1
01.
003
556.
31-9
.29
556.
2956
2.19
94.4
41.
003
NM
20.2
790.
01-7
.11
790.
0579
6.28
93.0
81.
003
556.
64-9
.46
556.
6156
2.31
94.4
61.
003
NM
30.1
793.
35-4
.86
793.
4179
8.57
93.2
01.
006
558.
43-7
.77
558.
4456
3.82
94.3
41.
005
NM
30.2
794.
31-4
.91
794.
3779
9.31
93.0
41.
007
559.
46-7
.77
559.
4656
4.34
94.3
81.
006
NM
40.1
796.
58-3
.25
796.
6580
1.20
93.2
01.
009
557.
66-9
.28
557.
6356
5.12
94.2
81.
008
NM
40.2
798.
71-3
.27
798.
7880
3.15
93.2
41.
012
558.
53-1
0.54
558.
4956
6.29
94.2
41.
010
NM
50.1
800.
78-1
.73
800.
8680
3.90
93.2
41.
012
561.
94-7
.85
561.
9556
6.99
94.2
41.
011
NM
50.2
806.
21-1
.16
806.
2980
8.18
93.0
81.
018
565.
62-7
.77
565.
6256
9.90
94.2
41.
016
NM
60.1
803.
41-1
.67
803.
4980
6.10
93.0
41.
015
563.
32-4
.77
563.
3656
9.00
94.3
21.
015
NM
60.2
812.
86-1
.44
812.
9481
3.96
92.7
21.
025
568.
81-5
.80
568.
8357
4.30
94.3
41.
024
NM
70.1
806.
541.
4480
6.62
808.
8193
.06
1.01
956
2.89
-7.9
956
2.89
569.
7794
.30
1.01
6N
M70.2
821.
890.
0182
1.97
822.
0193
.22
1.03
557
2.78
-11.
1857
2.73
578.
7594
.04
1.03
2N
M80.1
803.
00-0
.54
803.
0880
9.98
93.2
61.
020
568.
05-4
.44
568.
0957
1.53
94.2
41.
019
NM
80.2
821.
97-1
.28
822.
0583
1.81
93.2
81.
048
584.
05-2
.50
584.
1058
7.34
94.0
41.
047
NM
90.1
805.
142.
6080
5.21
812.
1193
.16
1.02
356
5.73
-5.9
956
5.76
572.
1694
.32
1.02
0N
M90.2
841.
104.
7984
1.17
846.
7593
.32
1.06
658
8.35
-7.0
858
8.36
595.
9494
.52
1.06
3
111
Tab
leE
52:
Infe
ren
cefo
rth
e95
thp
erce
nti
leeµ
+1.6
45σ
bas
edon
LN
(µ=
0,σ
2=
1)d
ata
wit
hC
=5.
18=
95th
per
centi
le
Res
ult
sfo
rn
=10
00R
esu
lts
forn
=20
00
RM
SE
Bia
sS
DS
DC
vg.
Rel
.R
MS
EB
ias
SD
SD
Cvg.
Rel
.×
103×
103
×10
3×
103
%L
en.
×10
3×
103
×10
3×
103
%L
en.
CD
251.7
6-4
.39
251.
7525
1.07
94.6
21.
000
177.
500.
4517
7.52
177.
7594
.94
1.00
0M
I.C
9026
7.4
4-7
.82
267.
3525
1.39
93.1
21.
001
187.
37-0
.06
187.
3917
8.07
93.4
21.
002
MI.
C80
276.4
41.
2327
6.46
252.
6792
.76
1.00
619
3.40
2.51
193.
4117
8.60
92.8
21.
005
MI.
D90
252.6
4-0
.60
252.
6725
2.11
94.6
41.
004
177.
922.
3717
7.92
178.
3195
.04
1.00
3M
I.D
8025
2.9
90.
6425
3.01
252.
8294
.72
1.00
717
8.63
3.17
178.
6217
8.74
94.9
81.
006
CE
NS
261.1
6-2
.95
261.
1726
0.61
94.6
61.
038
183.
052.
6418
3.05
184.
5295
.26
1.03
8N
M10
.125
2.0
3-4
.31
252.
0125
1.24
94.6
41.
001
177.
640.
5117
7.66
177.
8795
.08
1.00
1N
M10
.225
2.0
7-4
.27
252.
0625
1.25
94.6
01.
001
177.
660.
5217
7.67
177.
8795
.08
1.00
1N
M20
.125
2.4
6-4
.31
252.
4525
1.67
94.7
41.
002
178.
110.
6717
8.13
178.
1895
.00
1.00
2N
M20
.225
2.6
2-4
.29
252.
6025
1.73
94.7
41.
003
178.
160.
6217
8.17
178.
2294
.98
1.00
3N
M30
.125
2.7
1-4
.32
252.
7025
2.28
94.6
21.
005
178.
220.
6317
8.24
178.
6195
.02
1.00
5N
M30
.225
3.2
5-4
.26
253.
2425
2.51
94.6
21.
006
178.
560.
6417
8.58
178.
7795
.02
1.00
6N
M40
.125
4.0
0-3
.72
254.
0025
3.02
94.5
81.
008
178.
620.
7117
8.64
179.
1094
.90
1.00
8N
M40
.225
4.7
5-3
.63
254.
7525
3.63
94.6
21.
010
179.
180.
6417
9.20
179.
5394
.78
1.01
0N
M50
.125
4.3
5-3
.71
254.
3525
3.72
94.5
41.
011
178.
981.
1917
8.99
179.
6395
.12
1.01
1N
M50
.225
5.9
1-3
.90
255.
9025
5.00
94.6
61.
016
180.
471.
0618
0.48
180.
5495
.22
1.01
6N
M60
.125
5.6
8-4
.12
255.
6825
4.35
94.6
41.
013
178.
831.
2917
8.84
180.
1095
.10
1.01
3N
M60
.225
8.3
7-4
.48
258.
3625
6.77
94.7
81.
023
180.
511.
7618
0.52
181.
8595
.22
1.02
3N
M70
.125
5.2
2-4
.91
255.
2025
4.86
94.8
41.
015
180.
111.
8818
0.11
180.
5395
.26
1.01
6N
M70
.225
9.4
8-4
.66
259.
4625
9.13
94.7
01.
032
183.
461.
6918
3.47
183.
5394
.84
1.03
3N
M80
.125
6.1
8-3
.82
256.
1825
5.42
94.7
81.
017
181.
081.
3018
1.09
180.
8494
.92
1.01
7N
M80
.226
2.9
5-4
.03
262.
9526
2.34
94.8
01.
045
187.
151.
4818
7.16
185.
7694
.82
1.04
5N
M90
.125
5.3
9-3
.94
255.
3925
5.80
94.8
81.
019
180.
441.
6718
0.45
181.
1395
.16
1.01
9N
M90
.226
6.2
4-4
.58
266.
2326
6.47
94.9
61.
061
188.
032.
0018
8.04
188.
7595
.06
1.06
2
112
Tab
leE
53:
Infe
ren
cefo
rth
elo
gsc
ale
mea
nµ
bas
edon
LN
(µ=
0,σ
2=
1)d
ata
wit
hC
=3.
602
=90
thp
erce
nti
le
Res
ult
sfo
rn
=10
0R
esu
lts
forn
=20
0
RM
SE
Bia
sS
DS
DC
vg.
Rel
.R
MS
EB
ias
SD
SD
Cvg.
Rel
.×
103×
103
×10
3×
103
%L
en.
×10
3×
103×
103×
103
%L
en.
CD
99.6
8-1
.73
99.6
899
.19
94.7
01.
000
71.8
70.
4171
.88
70.3
794
.36
1.00
0M
I.C
90
101
.42
-2.3
010
1.40
99.2
994
.30
1.00
173
.00
0.19
73.0
070
.42
94.1
21.
001
MI.
C80
105
.18
3.28
105.
1410
0.00
93.7
81.
008
74.8
72.
6874
.83
70.7
293
.60
1.00
5M
I.D
90
99.7
3-1
.73
99.7
399
.79
94.7
41.
006
71.9
90.
4072
.00
70.5
994
.32
1.00
3M
I.D
80
100
.04
-1.5
610
0.04
100.
0394
.76
1.00
872
.03
0.40
72.0
370
.74
94.5
21.
005
CE
NS
100
.80
-0.8
210
0.81
100.
4094
.80
1.01
272
.70
0.69
72.7
071
.12
94.6
61.
011
NM
10.
199.6
7-1
.69
99.6
699
.21
94.7
41.
000
71.8
70.
4271
.87
70.3
894
.48
1.00
0N
M10.
299.6
6-1
.69
99.6
699
.21
94.7
41.
000
71.8
60.
4271
.87
70.3
894
.46
1.00
0N
M20.
199.7
6-1
.69
99.7
599
.25
94.6
21.
001
71.9
10.
4171
.92
70.4
194
.42
1.00
1N
M20.
299.7
7-1
.67
99.7
799
.26
94.6
41.
001
71.9
10.
3971
.92
70.4
194
.42
1.00
1N
M30.
199.7
8-1
.79
99.7
899
.29
94.7
61.
001
71.9
50.
3771
.96
70.4
494
.42
1.00
1N
M30.
299.7
9-1
.81
99.7
899
.32
94.7
21.
001
71.9
30.
3571
.94
70.4
694
.38
1.00
1N
M40.
199.7
9-1
.78
99.7
899
.36
94.6
01.
002
72.0
00.
5372
.00
70.5
194
.42
1.00
2N
M40.
299.7
7-1
.83
99.7
799
.43
94.7
01.
002
72.0
50.
5172
.05
70.5
694
.40
1.00
3N
M50.
1100
.01
-1.7
310
0.01
99.4
494
.68
1.00
372
.11
0.52
72.1
270
.56
94.3
21.
003
NM
50.
2100
.12
-1.7
610
0.12
99.6
094
.70
1.00
472
.27
0.55
72.2
770
.68
94.3
81.
004
NM
60.
199.9
9-1
.43
99.9
999
.56
94.7
01.
004
72.0
50.
4772
.06
70.6
094
.32
1.00
3N
M60.
2100
.31
-1.4
310
0.31
99.9
094
.82
1.00
772
.26
0.41
72.2
670
.84
94.5
21.
007
NM
70.
199.9
7-1
.53
99.9
799
.60
94.7
01.
004
72.1
60.
4172
.16
70.6
394
.50
1.00
4N
M70.
2100
.45
-1.6
710
0.44
100.
2394
.74
1.01
072
.57
0.50
72.5
871
.10
94.4
61.
010
NM
80.
1100
.01
-1.4
710
0.01
99.6
794
.56
1.00
572
.27
0.47
72.2
770
.67
94.3
81.
004
NM
80.
2101
.11
-1.4
610
1.11
100.
8494
.82
1.01
772
.94
0.60
72.9
571
.53
94.4
41.
016
NM
90.
1100
.07
-1.5
410
0.07
99.7
094
.56
1.00
572
.24
0.45
72.2
570
.70
94.5
01.
005
NM
90.
2101
.74
-1.6
110
1.74
101.
8594
.82
1.02
773
.81
0.77
73.8
172
.28
94.8
41.
027
113
Tab
leE
54:
Infe
ren
cefo
rth
elo
gsc
ale
mea
nµ
bas
edon
LN
(µ=
0,σ
2=
1)d
ata
wit
hC
=3.
602
=90
thp
erce
nti
le
Res
ult
sfo
rn
=10
00R
esu
lts
forn
=20
00
RM
SE
Bia
sS
DS
DC
vg.
Rel
.R
MS
EB
ias
SD
SD
Cvg.
Rel
.×
103
×10
3×
103×
103
%L
en.
×10
3×
103×
103×
103
%L
en.
CD
31.2
3-0
.02
31.2
331
.61
94.8
81.
000
22.5
40.
2022
.54
22.3
594
.78
1.00
0M
I.C
90
31.7
0-0
.05
31.7
131
.63
94.6
41.
001
22.9
20.
2322
.92
22.3
694
.54
1.00
1M
I.C
80
32.2
00.
4632
.20
31.6
994
.20
1.00
323
.34
0.51
23.3
322
.40
94.2
61.
002
MI.
D90
31.2
7-0
.07
31.2
731
.64
95.0
01.
001
22.5
70.
2022
.57
22.3
794
.78
1.00
1M
I.D
80
31.3
5-0
.01
31.3
531
.70
94.8
21.
003
22.5
60.
2022
.56
22.4
194
.94
1.00
3C
EN
S31
.58
0.16
31.5
831
.93
94.8
01.
010
22.7
70.
3222
.77
22.5
894
.86
1.01
0N
M10.
131
.23
-0.0
331
.23
31.6
194
.92
1.00
022
.54
0.19
22.5
522
.35
94.8
41.
000
NM
10.
231
.23
-0.0
331
.24
31.6
194
.94
1.00
022
.55
0.19
22.5
522
.35
94.7
81.
000
NM
20.
131
.24
-0.0
331
.24
31.6
295
.02
1.00
122
.56
0.21
22.5
622
.36
94.7
21.
001
NM
20.
231
.24
-0.0
431
.24
31.6
294
.94
1.00
122
.56
0.20
22.5
622
.36
94.7
61.
001
NM
30.
131
.27
0.00
31.2
731
.64
95.0
21.
001
22.5
70.
1822
.58
22.3
794
.76
1.00
1N
M30.
231
.26
-0.0
031
.27
31.6
595
.02
1.00
122
.59
0.19
22.5
922
.38
94.8
41.
001
NM
40.
131
.29
-0.0
131
.30
31.6
695
.04
1.00
222
.60
0.21
22.6
022
.39
94.7
41.
002
NM
40.
231
.31
-0.0
331
.31
31.6
995
.10
1.00
322
.63
0.21
22.6
322
.40
94.8
21.
003
NM
50.
131
.30
0.00
31.3
031
.69
95.0
41.
003
22.5
80.
1822
.58
22.4
095
.06
1.00
2N
M50.
231
.34
-0.0
431
.34
31.7
495
.10
1.00
422
.62
0.19
22.6
222
.44
94.8
41.
004
NM
60.
131
.35
0.02
31.3
631
.71
94.9
01.
003
22.6
00.
2222
.60
22.4
294
.94
1.00
3N
M60.
231
.43
-0.0
431
.44
31.8
295
.10
1.00
722
.70
0.19
22.7
122
.50
94.7
41.
007
NM
70.
131
.33
0.09
31.3
331
.73
94.9
41.
004
22.6
10.
2422
.61
22.4
394
.88
1.00
4N
M70.
231
.50
0.12
31.5
031
.94
94.9
81.
011
22.7
60.
2522
.76
22.5
895
.02
1.01
0N
M80.
131
.36
-0.0
031
.36
31.7
494
.92
1.00
422
.69
0.25
22.6
922
.44
94.8
01.
004
NM
80.
231
.77
-0.1
231
.77
32.1
295
.18
1.01
622
.92
0.25
22.9
222
.71
95.0
81.
016
NM
90.
131
.41
0.07
31.4
231
.76
94.9
21.
005
22.6
20.
2422
.62
22.4
594
.92
1.00
5N
M90.
232
.17
-0.0
032
.17
32.4
695
.04
1.02
723
.16
0.21
23.1
622
.95
94.9
21.
027
114
Tab
leE
55:
Infe
ren
cefo
rth
elo
gsc
ale
vari
anceσ
2b
ased
onLN
(µ=
0,σ
2=
1)d
ata
wit
hC
=3.
602
=90
thp
erce
nti
le
Res
ult
sfo
rn
=10
0R
esu
lts
forn
=20
0
RM
SE
Bia
sS
DS
DC
vg.
Rel
.R
MS
EB
ias
SD
SD
Cvg.
Rel
.×
103
×10
3×
103
×10
3%
Len
.×
103×
103
×10
3×
103
%L
en.
CD
140.
77-1
1.19
140.
3413
9.84
93.1
21.
000
98.4
8-7
.15
98.2
399
.28
94.4
81.
000
MI.
C90
154.
77-9
.50
154.
4914
1.11
91.0
41.
009
108.
43-6
.43
108.
2599
.89
92.2
41.
006
MI.
C80
156.
231.
7315
6.24
143.
6591
.50
1.02
710
9.33
-0.8
810
9.34
100.
9592
.12
1.01
7M
I.D
90
144.
43-1
.11
144.
4414
3.03
93.7
81.
023
99.1
3-2
.85
99.1
010
0.31
94.6
61.
010
MI.
D80
143.
42-0
.15
143.
4414
3.06
93.6
41.
023
99.4
2-1
.93
99.4
110
0.64
94.8
41.
014
CE
NS
151.
96-7
.03
151.
8115
2.37
93.4
61.
090
107.
77-5
.99
107.
6110
7.71
94.2
41.
085
NM
10.1
140.
95-1
0.97
140.
5314
0.01
93.0
81.
001
98.5
7-7
.12
98.3
299
.39
94.4
61.
001
NM
10.
2140.
95-1
0.98
140.
5314
0.02
93.0
41.
001
98.5
8-7
.13
98.3
399
.39
94.4
81.
001
NM
20.
1141.
55-1
1.03
141.
1314
0.40
93.0
21.
004
98.8
2-7
.19
98.5
799
.66
94.4
61.
004
NM
20.
2141.
59-1
0.98
141.
1814
0.44
93.0
01.
004
98.8
4-7
.22
98.5
899
.69
94.5
21.
004
NM
30.
1142.
08-1
1.28
141.
6514
0.95
93.1
61.
008
99.0
6-7
.33
98.8
010
0.07
94.5
81.
008
NM
30.
2142.
32-1
1.33
141.
8814
1.07
93.1
41.
009
99.2
1-7
.37
98.9
410
0.15
94.6
01.
009
NM
40.
1142.
25-1
1.15
141.
8314
1.67
93.0
01.
013
99.9
6-6
.70
99.7
410
0.64
94.2
81.
014
NM
40.
2142.
61-1
1.28
142.
1714
1.99
93.0
41.
015
100.
25-6
.75
100.
0310
0.87
94.2
61.
016
NM
50.1
142.
19-1
1.08
141.
7714
2.44
93.3
61.
019
100.
36-6
.79
100.
1410
1.17
94.5
41.
019
NM
50.2
143.
14-1
1.20
142.
7114
3.16
93.3
21.
024
100.
79-6
.72
100.
5810
1.70
94.2
61.
024
NM
60.1
144.
51-9
.78
144.
1914
3.39
93.2
61.
025
101.
22-6
.93
100.
9910
1.69
94.2
01.
024
NM
60.2
145.
89-9
.84
145.
5714
4.77
93.0
21.
035
102.
24-7
.09
102.
0010
2.66
93.8
81.
034
NM
70.1
144.
39-1
0.19
144.
0414
4.03
93.3
21.
030
101.
27-7
.18
101.
0310
2.16
94.3
41.
029
NM
70.2
147.
47-1
0.55
147.
1114
6.38
93.2
41.
047
102.
76-7
.02
102.
5310
3.90
94.5
41.
046
NM
80.1
144.
95-9
.84
144.
6314
4.70
93.2
61.
035
101.
50-7
.00
101.
2610
2.61
94.4
01.
033
NM
80.2
149.
14-9
.91
148.
8214
8.51
93.0
81.
062
104.
18-6
.75
103.
9710
5.38
94.5
41.
061
NM
90.1
144.
52-1
0.28
144.
1614
5.15
93.5
61.
038
102.
68-7
.03
102.
4510
2.97
94.2
01.
037
NM
90.2
149.
56-1
0.76
149.
1815
0.55
93.4
21.
077
106.
94-6
.63
106.
7410
6.95
94.0
21.
077
115
Tab
leE
56:
Infe
ren
cefo
rth
elo
gsc
ale
vari
anceσ
2b
ased
onLN
(µ=
0,σ
2=
1)d
ata
wit
hC
=3.
602
=90
thp
erce
nti
le
Res
ult
sfo
rn
=10
00R
esu
lts
forn
=20
00
RM
SE
Bia
sS
DS
DC
vg.
Rel
.R
MS
EB
ias
SD
SD
Cvg.
Rel
.×
103
×10
3×
103×
103
%L
en.
×10
3×
103×
103×
103
%L
en.
CD
44.7
8-0
.60
44.7
844
.69
94.6
61.
000
31.4
5-1
.04
31.4
431
.59
94.8
21.
000
MI.
C90
48.8
8-0
.24
48.8
944
.88
92.6
01.
004
34.2
8-0
.70
34.2
731
.71
92.7
41.
004
MI.
C80
49.2
70.
9549
.26
45.1
092
.64
1.00
934
.49
-0.1
034
.49
31.8
593
.08
1.00
8M
I.D
90
44.8
90.
0844
.89
44.9
194
.46
1.00
531
.60
-0.6
431
.59
31.7
294
.80
1.00
4M
I.D
80
45.1
50.
4045
.15
45.0
194
.58
1.00
731
.60
-0.5
531
.60
31.7
995
.00
1.00
6C
EN
S48
.41
0.18
48.4
248
.44
94.7
81.
084
34.0
9-0
.53
34.0
934
.22
94.7
41.
083
NM
10.
144
.82
-0.6
144
.82
44.7
494
.58
1.00
131
.47
-1.0
831
.46
31.6
294
.70
1.00
1N
M10.
244
.82
-0.6
244
.82
44.7
494
.56
1.00
131
.47
-1.0
831
.46
31.6
294
.70
1.00
1N
M20.
144
.97
-0.6
044
.97
44.8
794
.52
1.00
431
.61
-1.0
131
.60
31.7
194
.74
1.00
4N
M20.
245
.00
-0.6
345
.00
44.8
894
.56
1.00
431
.62
-1.0
231
.61
31.7
294
.72
1.00
4N
M30.
145
.07
-0.5
045
.07
45.0
694
.88
1.00
831
.78
-1.1
231
.76
31.8
494
.60
1.00
8N
M30.
245
.14
-0.5
245
.14
45.1
094
.82
1.00
931
.80
-1.1
031
.78
31.8
794
.64
1.00
9N
M40.
145
.37
-0.5
345
.37
45.2
994
.70
1.01
331
.90
-1.0
131
.89
32.0
194
.54
1.01
3N
M40.
245
.51
-0.5
745
.51
45.3
994
.70
1.01
631
.96
-1.0
231
.95
32.0
894
.64
1.01
6N
M50.
145
.49
-0.4
745
.49
45.5
494
.70
1.01
932
.02
-1.1
032
.01
32.1
894
.66
1.01
9N
M50.
245
.82
-0.5
745
.82
45.7
794
.66
1.02
432
.17
-1.0
832
.15
32.3
494
.80
1.02
4N
M60.
145
.78
-0.4
445
.79
45.7
894
.84
1.02
432
.30
-0.9
232
.29
32.3
594
.64
1.02
4N
M60.
246
.33
-0.5
846
.33
46.2
294
.66
1.03
432
.50
-1.0
032
.49
32.6
794
.72
1.03
4N
M70.
145
.94
-0.1
345
.94
46.0
294
.84
1.03
032
.39
-0.9
032
.38
32.5
194
.74
1.02
9N
M70.
246
.88
-0.0
646
.89
46.8
094
.82
1.04
733
.00
-0.8
732
.99
33.0
694
.76
1.04
7N
M80.
146
.13
-0.4
946
.13
46.1
994
.94
1.03
432
.60
-0.8
332
.59
32.6
594
.52
1.03
4N
M80.
247
.46
-0.7
847
.46
47.4
294
.98
1.06
133
.41
-0.8
233
.40
33.5
394
.72
1.06
1N
M90.
146
.16
-0.2
146
.17
46.3
794
.72
1.03
732
.69
-0.8
732
.68
32.7
694
.46
1.03
7N
M90.
248
.10
-0.4
248
.11
48.1
495
.02
1.07
733
.86
-0.9
533
.85
34.0
294
.70
1.07
7
116
Tab
leE
57:
Infe
ren
cefo
rth
em
eaneµ
+σ2/2
bas
edon
LN
(µ=
0,σ
2=
1)d
ata
wit
hC
=3.
602
=90
thp
erce
nti
le
Res
ult
sfo
rn
=10
0R
esu
lts
forn
=20
0
RM
SE
Bia
sS
DS
DC
vg.
Rel
.R
MS
EB
ias
SD
SD
Cvg.
Rel
.×
103
×10
3×
103
×10
3%
Len
.×
103×
103
×10
3×
103
%L
en.
CD
202.0
40.
2020
2.06
201.
5693
.24
1.00
014
3.17
0.96
143.
1814
2.56
94.3
61.
000
MI.
C90
222.9
36.
9122
2.85
206.
2692
.10
1.02
315
5.82
4.09
155.
7814
4.28
92.8
21.
012
MI.
C80
240.1
832
.76
237.
9621
5.24
92.3
01.
068
164.
3116
.03
163.
5414
7.52
92.6
41.
035
MI.
D90
6×
1021
9×
1019
6×
1021
5×
1021
93.9
02×
1019
145.
446.
9514
5.29
145.
0294
.60
1.01
7M
I.D
80
212.0
219
.65
211.
1321
2.08
94.1
01.
052
146.
569.
7514
6.25
146.
4295
.02
1.02
7C
EN
S21
7.1
06.
8021
7.02
216.
6693
.58
1.07
515
4.19
3.29
154.
1715
2.04
94.5
41.
067
NM
10.
120
2.1
90.
4720
2.21
201.
7993
.30
1.00
114
3.20
1.00
143.
2114
2.68
94.3
41.
001
NM
10.
220
2.1
80.
4720
2.20
201.
8093
.22
1.00
114
3.19
0.99
143.
2014
2.69
94.4
21.
001
NM
20.
120
3.0
50.
5220
3.07
202.
2593
.18
1.00
314
3.62
0.96
143.
6314
2.99
94.4
81.
003
NM
20.
220
3.1
30.
6120
3.15
202.
3393
.14
1.00
414
3.62
0.91
143.
6314
3.02
94.3
61.
003
NM
30.
120
3.4
90.
2220
3.51
202.
8593
.22
1.00
614
3.88
0.79
143.
9014
3.43
94.6
21.
006
NM
30.
220
3.6
90.
1720
3.71
203.
0493
.10
1.00
714
3.94
0.74
143.
9514
3.56
94.5
01.
007
NM
40.
120
3.6
10.
3520
3.63
203.
6793
.00
1.01
014
4.84
1.67
144.
8414
4.13
94.4
41.
011
NM
40.
220
3.8
20.
1820
3.84
204.
1793
.04
1.01
314
5.25
1.63
145.
2614
4.50
94.2
61.
014
NM
50.
120
4.5
50.
6020
4.57
204.
5893
.54
1.01
514
5.65
1.63
145.
6614
4.72
94.2
61.
015
NM
50.
220
5.6
80.
5820
5.70
205.
7493
.24
1.02
114
6.50
1.82
146.
5014
5.57
94.4
81.
021
NM
60.
120
6.6
82.
3720
6.69
205.
8893
.18
1.02
114
5.94
1.47
145.
9514
5.28
94.4
81.
019
NM
60.
220
9.0
22.
6020
9.03
208.
1893
.16
1.03
314
7.46
1.38
147.
4714
6.86
94.3
61.
030
NM
70.
120
6.4
81.
8620
6.49
206.
5393
.30
1.02
514
6.53
1.22
146.
5414
5.78
94.2
81.
023
NM
70.
221
0.5
41.
8421
0.55
210.
5793
.28
1.04
514
9.06
1.71
149.
0614
8.71
94.5
01.
043
NM
80.
120
7.0
92.
3020
7.10
207.
3493
.36
1.02
914
7.16
1.51
147.
1714
6.30
94.3
81.
026
NM
80.
221
4.3
83.
1421
4.38
214.
3393
.14
1.06
315
1.57
2.31
151.
5615
1.24
94.3
61.
061
NM
90.
120
6.9
21.
8120
6.93
207.
7993
.14
1.03
114
8.05
1.53
148.
0614
6.70
94.4
61.
029
NM
90.
221
6.0
12.
4321
6.02
218.
7493
.56
1.08
515
6.18
3.10
156.
1715
4.65
94.3
21.
085
117
Tab
leE
58:
Infe
ren
cefo
rth
em
eaneµ
+σ2/2
bas
edon
LN
(µ=
0,σ
2=
1)d
ata
wit
hC
=3.
602
=90
thp
erce
nti
le
Res
ult
sfo
rn
=10
00R
esu
lts
forn
=20
00
RM
SE
Bia
sS
DS
DC
vg.
Rel
.R
MS
EB
ias
SD
SD
Cvg.
Rel
.×
103
×10
3×
103×
103
%L
en.
×10
3×
103×
103×
103
%L
en.
CD
62.8
40.
6662
.84
63.8
995
.36
1.00
044
.83
0.08
44.8
445
.13
95.1
81.
000
MI.
C90
67.7
61.
4667
.75
64.2
093
.24
1.00
548
.34
0.68
48.3
445
.32
93.3
61.
004
MI.
C80
69.6
93.
8669
.59
64.6
993
.30
1.01
349
.67
1.91
49.6
445
.58
92.7
21.
010
MI.
D90
63.1
61.
5863
.14
64.2
595
.36
1.00
645
.09
0.63
45.0
945
.34
95.2
61.
005
MI.
D80
63.6
72.
3663
.63
64.5
695
.34
1.01
145
.10
0.90
45.1
045
.52
95.1
61.
009
CE
NS
66.9
71.
7666
.96
67.9
195
.28
1.06
347
.65
0.78
47.6
547
.94
94.9
41.
062
NM
10.
162
.88
0.64
62.8
863
.94
95.2
21.
001
44.8
70.
0444
.87
45.1
795
.18
1.00
1N
M10.
262
.89
0.64
62.8
963
.94
95.2
81.
001
44.8
70.
0444
.88
45.1
795
.16
1.00
1N
M20.
163
.03
0.66
63.0
364
.08
95.2
61.
003
45.0
20.
1245
.03
45.2
795
.14
1.00
3N
M20.
263
.04
0.62
63.0
464
.10
95.3
21.
003
45.0
30.
1145
.03
45.2
895
.20
1.00
3N
M30.
163
.22
0.80
63.2
264
.30
95.4
21.
006
45.2
0-0
.00
45.2
145
.41
95.1
81.
006
NM
30.
263
.27
0.78
63.2
764
.36
95.4
01.
007
45.2
60.
0245
.27
45.4
695
.02
1.00
7N
M40.
163
.54
0.77
63.5
464
.55
95.2
41.
010
45.4
00.
1445
.40
45.5
995
.06
1.01
0N
M40.
263
.70
0.72
63.7
064
.71
95.3
41.
013
45.5
50.
1345
.55
45.7
195
.20
1.01
3N
M50.
163
.65
0.84
63.6
564
.81
95.3
01.
014
45.4
00.
0245
.41
45.7
794
.98
1.01
4N
M50.
264
.05
0.71
64.0
565
.17
95.2
61.
020
45.6
40.
0645
.64
46.0
394
.98
1.02
0N
M60.
164
.09
0.90
64.0
965
.08
95.1
61.
019
45.6
90.
2445
.70
45.9
795
.18
1.01
8N
M60.
264
.81
0.73
64.8
165
.78
95.2
61.
030
46.1
70.
1446
.17
46.4
795
.44
1.03
0N
M70.
164
.16
1.28
64.1
565
.34
95.5
41.
023
45.8
00.
2845
.80
46.1
494
.98
1.02
2N
M70.
265
.50
1.45
65.4
966
.63
95.4
01.
043
46.7
90.
3646
.80
47.0
494
.88
1.04
2N
M80.
164
.37
0.85
64.3
765
.52
95.1
81.
025
46.2
40.
3846
.24
46.2
994
.88
1.02
6N
M80.
266
.68
0.51
66.6
967
.65
95.5
21.
059
47.6
10.
4247
.62
47.8
195
.22
1.05
9N
M90.
164
.61
1.20
64.6
065
.71
95.3
81.
029
46.0
20.
3346
.02
46.4
095
.22
1.02
8N
M90.
268
.31
1.06
68.3
169
.15
95.1
41.
082
48.4
80.
2748
.48
48.8
495
.20
1.08
2
118
Tab
leE
59:
Infe
ren
cefo
rth
eva
rian
cee2µ
+2σ2−e2µ
+σ2
bas
edon
LN
(µ=
0,σ
2=
1)d
ata
wit
hC
=3.
602
=90
thp
erce
nti
le
Res
ult
sfo
rn
=10
0R
esu
lts
forn
=20
0
RM
SE
Bia
sS
DS
DC
vg.
Rel
.R
MS
EB
ias
SD
SD
Cvg.
Rel
.×
103
×10
3×
103
×10
3%
Len
.×
103
×10
3×
103
×10
3%
Len
.
CD
214
8.4
921
6.4
621
37.7
720
85.7
988
.92
1.00
014
27.9
795
.62
1424
.91
1418
.54
91.4
61.
000
MI.
C90
277
2.2
254
5.5
427
18.2
824
86.2
487
.92
1.19
216
97.1
523
4.11
1681
.10
1528
.93
90.9
01.
078
MI.
C80
329
9.2
1106
2.8
131
23.6
530
58.7
090
.64
1.46
619
03.7
645
3.04
1849
.25
1681
.33
92.5
01.
185
MI.
D90
6×
1089
9×
108
76×
1089
2×
1090
91.7
89×
1986
1533
.35
253.
9615
12.3
315
41.8
392
.92
1.08
7M
I.D
80273
8.9
279
1.5
926
22.3
027
87.0
792
.76
1.33
615
88.1
233
1.00
1553
.40
1607
.07
93.7
61.
133
CE
NS
249
3.0
335
7.9
424
67.4
523
88.7
888
.72
1.14
516
43.8
915
5.73
1636
.67
1581
.10
91.4
61.
115
NM
10.1
215
2.9
722
0.4
721
41.8
720
90.3
588
.70
1.00
214
28.6
996
.28
1425
.58
1420
.43
91.4
61.
001
NM
10.2
215
3.1
822
0.4
621
42.0
820
90.4
288
.72
1.00
214
28.5
696
.19
1425
.46
1420
.45
91.4
61.
001
NM
20.1
217
2.0
622
4.3
621
60.6
520
99.4
988
.88
1.00
714
36.5
596
.83
1433
.43
1425
.23
91.4
21.
005
NM
20.2
217
2.9
822
5.5
021
61.4
721
00.7
388
.86
1.00
714
36.8
796
.32
1433
.78
1425
.51
91.4
21.
005
NM
30.1
217
2.6
822
2.7
421
61.4
421
08.7
788
.78
1.01
114
37.6
195
.46
1434
.58
1431
.44
91.5
01.
009
NM
30.2
217
6.2
322
3.1
221
64.9
821
11.5
088
.64
1.01
214
39.6
495
.31
1436
.63
1433
.13
91.6
41.
010
NM
40.1
217
7.6
722
5.2
121
66.2
121
22.2
088
.86
1.01
714
58.2
010
8.58
1454
.30
1444
.58
90.9
81.
018
NM
40.2
217
9.8
522
4.5
721
68.4
721
28.3
888
.82
1.02
014
64.3
710
9.19
1460
.44
1449
.35
91.2
61.
022
NM
50.1
218
7.1
822
9.2
221
75.3
621
37.4
588
.88
1.02
514
71.2
110
9.80
1467
.25
1453
.91
91.4
01.
025
NM
50.2
220
3.9
823
3.2
921
91.8
221
53.9
488
.78
1.03
314
82.9
511
3.55
1478
.75
1465
.08
91.1
41.
033
NM
60.1
225
8.1
426
1.9
522
43.1
221
69.8
688
.78
1.04
014
75.8
510
9.76
1471
.91
1462
.72
91.4
01.
031
NM
60.2
229
6.6
727
2.1
222
80.7
222
02.9
088
.78
1.05
614
98.8
611
2.44
1494
.79
1482
.65
91.4
61.
045
NM
70.1
224
5.8
125
4.7
122
31.5
421
78.2
688
.94
1.04
414
88.1
810
7.81
1484
.42
1470
.23
91.5
41.
036
NM
70.2
231
4.2
127
0.3
322
98.5
922
36.0
788
.64
1.07
215
23.3
111
8.71
1518
.83
1507
.56
91.9
61.
063
NM
80.1
226
3.0
026
3.2
222
47.8
721
94.3
888
.88
1.05
214
95.2
411
2.27
1491
.17
1478
.98
91.5
41.
043
NM
80.2
238
4.5
629
6.8
823
66.2
422
93.9
988
.36
1.10
015
58.5
113
0.98
1553
.15
1541
.00
91.6
21.
086
NM
90.1
224
1.9
525
4.3
822
27.6
921
98.4
788
.96
1.05
415
20.0
511
6.21
1515
.75
1486
.90
91.5
61.
048
NM
90.2
237
2.4
028
8.4
923
55.0
323
39.6
788
.80
1.12
216
27.4
414
9.48
1620
.72
1583
.48
91.0
81.
116
119
Tab
leE
60:
Infe
ren
cefo
rth
eva
rian
cee2µ
+2σ2−e2µ
+σ2
bas
edon
LN
(µ=
0,σ
2=
1)d
ata
wit
hC
=3.
602
=90
thp
erce
nti
le
Res
ult
sfo
rn
=10
00R
esu
lts
forn
=20
00
RM
SE
Bia
sS
DS
DC
vg.
Rel
.R
MS
EB
ias
SD
SD
Cvg.
Rel
.×
10
3×
103
×10
3×
103
%L
en.
×10
3×
103
×10
3×
103
%L
en.
CD
617
.36
28.0
461
6.78
620.
3394
.74
1.00
043
1.88
6.94
431.
8743
5.86
94.8
61.
000
MI.
C90
689
.99
54.9
668
7.87
630.
9392
.62
1.01
747
9.65
22.5
147
9.17
440.
6392
.68
1.01
1M
I.C
80
715
.76
94.5
270
9.56
644.
4392
.82
1.03
949
2.50
42.1
149
0.75
446.
3093
.04
1.02
4M
I.D
90
626
.87
53.0
162
4.69
631.
1495
.06
1.01
743
6.98
20.2
043
6.56
440.
6695
.10
1.01
1M
I.D
80
636
.15
70.2
763
2.32
638.
4495
.08
1.02
943
8.18
27.3
143
7.37
443.
7395
.28
1.01
8C
EN
S678
.59
46.1
967
7.08
679.
8094
.74
1.09
647
2.95
17.7
547
2.66
476.
3294
.58
1.09
3N
M10.
1617
.98
27.9
261
7.41
621.
0394
.74
1.00
143
2.18
6.51
432.
1843
6.32
94.7
81.
001
NM
10.
2618
.10
27.8
461
7.53
621.
0494
.70
1.00
143
2.19
6.50
432.
1843
6.33
94.7
21.
001
NM
20.
1620
.05
28.3
161
9.47
623.
0794
.50
1.00
443
4.48
7.62
434.
4643
7.82
94.5
01.
005
NM
20.
2620
.33
27.9
061
9.77
623.
2094
.54
1.00
543
4.64
7.54
434.
6243
7.96
94.4
41.
005
NM
30.
1622
.74
30.1
162
2.07
626.
2694
.80
1.01
043
6.90
6.27
436.
9043
9.71
94.8
81.
009
NM
30.
2623
.71
29.8
962
3.06
626.
9894
.82
1.01
143
7.59
6.57
437.
5844
0.27
94.8
01.
010
NM
40.
1627
.16
30.2
262
6.49
629.
7994
.72
1.01
543
9.31
8.05
439.
2844
2.36
94.7
61.
015
NM
40.
2629
.37
29.7
862
8.73
631.
7094
.52
1.01
844
0.89
8.06
440.
8644
3.75
94.8
21.
018
NM
50.
1629
.12
31.1
762
8.41
633.
6994
.62
1.02
243
9.97
6.80
439.
9644
4.84
94.8
41.
021
NM
50.
2634
.66
30.2
863
4.00
637.
8494
.50
1.02
844
2.72
7.32
442.
7044
7.92
94.7
41.
028
NM
60.
1634
.40
32.2
963
3.64
637.
5794
.52
1.02
844
4.82
9.65
444.
7644
7.74
94.7
61.
027
NM
60.
2643
.49
31.3
064
2.79
645.
6794
.50
1.04
144
9.61
8.86
449.
5645
3.46
94.7
61.
040
NM
70.
1637
.19
36.9
263
6.18
641.
7394
.90
1.03
444
6.21
10.1
844
6.14
450.
1794
.82
1.03
3N
M70.
2654
.31
40.1
865
3.14
656.
8594
.76
1.05
945
8.13
11.7
345
8.03
460.
6094
.80
1.05
7N
M80.
1638
.82
32.1
563
8.07
643.
8794
.68
1.03
845
0.65
11.6
245
0.54
452.
3894
.50
1.03
8N
M80.
2664
.63
30.7
766
3.98
667.
5794
.56
1.07
646
6.23
13.0
346
6.09
469.
3994
.48
1.07
7N
M90.
1641
.44
36.4
264
0.47
647.
0294
.50
1.04
344
9.81
10.9
844
9.73
454.
0094
.76
1.04
2N
M90.
2680
.84
38.2
367
9.83
683.
7194
.58
1.10
247
4.83
11.9
047
4.73
479.
6794
.82
1.10
1
120
Tab
leE
61:
Infe
ren
cefo
rth
e84
thp
erce
nti
leeµ
+σ
bas
edon
LN
(µ=
0,σ
2=
1)d
ata
wit
hC
=3.
602
=90
thp
erce
nti
le
Res
ult
sfo
rn
=10
0R
esu
lts
forn
=20
0
RM
SE
Bia
sS
DS
DC
vg.
Rel
.R
MS
EB
ias
SD
SD
Cvg.
Rel
.×
103×
103
×10
3×
103
%L
en.
×10
3×
103
×10
3×
103
%L
en.
CD
332.2
1-6
.45
332.
1833
1.10
93.2
21.
000
235.
75-1
.74
235.
7723
4.69
94.3
41.
000
MI.
C90
363.8
40.
3836
3.87
336.
5491
.72
1.01
625
5.65
1.46
255.
6723
6.82
92.6
81.
009
MI.
C80
389.0
540
.02
387.
0334
8.58
92.0
01.
053
268.
2619
.80
267.
5624
1.31
92.4
81.
028
MI.
D90
2726
.01
50.9
427
25.8
168
3.43
93.8
22.
064
238.
706.
6923
8.63
237.
9794
.56
1.01
4M
I.D
80
344.8
720
.84
344.
2734
4.68
93.8
01.
041
240.
2210
.70
240.
0023
9.94
94.9
41.
022
CE
NS
355.5
93.
2535
5.62
354.
8893
.50
1.07
225
3.22
1.43
253.
2424
9.98
94.5
01.
065
NM
10.
133
2.4
4-6
.03
332.
4233
1.46
93.2
61.
001
235.
81-1
.68
235.
8223
4.89
94.4
01.
001
NM
10.
233
2.4
3-6
.03
332.
4133
1.47
93.2
61.
001
235.
79-1
.69
235.
8123
4.90
94.3
81.
001
NM
20.
133
3.7
8-6
.01
333.
7633
2.20
93.0
61.
003
236.
45-1
.75
236.
4723
5.40
94.4
41.
003
NM
20.
233
3.8
9-5
.87
333.
8733
2.32
93.1
21.
004
236.
46-1
.84
236.
4823
5.45
94.4
01.
003
NM
30.
133
4.6
0-6
.56
334.
5633
3.18
93.1
61.
006
236.
93-2
.05
236.
9523
6.12
94.5
41.
006
NM
30.
233
4.9
3-6
.66
334.
8933
3.50
93.1
21.
007
237.
02-2
.14
237.
0323
6.34
94.5
21.
007
NM
40.
133
4.7
7-6
.36
334.
7433
4.52
93.0
81.
010
238.
43-0
.67
238.
4523
7.24
94.4
41.
011
NM
40.
233
5.1
4-6
.67
335.
1133
5.34
93.0
61.
013
239.
11-0
.76
239.
1323
7.85
94.3
61.
013
NM
50.
133
6.2
8-5
.94
336.
2633
5.99
93.4
01.
015
239.
73-0
.75
239.
7623
8.20
94.2
21.
015
NM
50.
233
8.1
5-6
.06
338.
1333
7.88
93.1
21.
021
241.
11-0
.48
241.
1323
9.59
94.3
41.
021
NM
60.
133
9.4
0-3
.26
339.
4233
7.96
93.2
21.
021
240.
27-1
.08
240.
2923
9.11
94.4
01.
019
NM
60.
234
3.2
0-3
.02
343.
2234
1.72
93.1
21.
032
242.
75-1
.30
242.
7824
1.71
94.2
81.
030
NM
70.
133
9.1
5-4
.09
339.
1633
9.04
93.3
01.
024
241.
15-1
.51
241.
1723
9.93
94.3
01.
022
NM
70.
234
5.7
7-4
.43
345.
7734
5.64
93.3
21.
044
245.
26-0
.80
245.
2924
4.74
94.4
21.
043
NM
80.
134
0.1
0-3
.42
340.
1234
0.32
93.3
21.
028
242.
18-1
.04
242.
2124
0.77
94.3
81.
026
NM
80.
235
1.8
4-2
.47
351.
8735
1.69
93.1
01.
062
249.
360.
1024
9.39
248.
8794
.34
1.06
0N
M90.
133
9.9
9-4
.19
340.
0034
1.08
93.1
21.
030
243.
56-1
.09
243.
5824
1.41
94.5
01.
029
NM
90.
235
4.9
2-3
.67
354.
9335
8.96
93.5
01.
084
256.
841.
1925
6.86
254.
4294
.28
1.08
4
121
Tab
leE
62:
Infe
ren
cefo
rth
e84
thp
erce
nti
leeµ
+σ
bas
edon
LN
(µ=
0,σ
2=
1)d
ata
wit
hC
=3.
602
=90
thp
erce
nti
le
Res
ult
sfo
rn
=10
00R
esu
lts
forn
=20
00
RM
SE
Bia
sS
DS
DC
vg.
Rel
.R
MS
EB
ias
SD
SD
Cvg.
Rel
.×
103×
103
×10
3×
103
%L
en.
×10
3×
103×
103×
103
%L
en.
CD
103
.55
0.40
103.
5610
5.29
95.3
81.
000
73.9
1-0
.20
73.9
174
.41
95.2
01.
000
MI.
C90
111
.59
1.36
111.
5910
5.73
93.2
01.
004
79.6
80.
6179
.68
74.6
893
.34
1.00
4M
I.C
80
114
.66
5.06
114.
5610
6.47
93.2
01.
011
81.8
42.
5281
.81
75.0
992
.70
1.00
9M
I.D
90
104
.01
1.67
104.
0010
5.83
95.3
61.
005
74.3
10.
5874
.31
74.7
395
.24
1.00
4M
I.D
80
104
.83
2.83
104.
8010
6.31
95.3
21.
010
74.3
20.
9774
.32
75.0
195
.12
1.00
8C
EN
S110
.31
2.11
110.
3011
1.88
95.2
41.
063
78.5
40.
8978
.54
79.0
194
.92
1.06
2N
M10.
1103
.62
0.38
103.
6310
5.37
95.2
41.
001
73.9
6-0
.27
73.9
774
.46
95.2
01.
001
NM
10.
2103
.63
0.36
103.
6410
5.37
95.3
01.
001
73.9
7-0
.27
73.9
874
.47
95.1
41.
001
NM
20.
1103
.87
0.40
103.
8810
5.61
95.2
81.
003
74.2
2-0
.14
74.2
374
.63
95.1
61.
003
NM
20.
2103
.88
0.33
103.
8910
5.63
95.2
21.
003
74.2
3-0
.15
74.2
474
.65
95.1
41.
003
NM
30.
1104
.17
0.63
104.
1810
5.96
95.3
81.
006
74.5
1-0
.35
74.5
274
.87
95.1
41.
006
NM
30.
2104
.25
0.59
104.
2610
6.06
95.4
01.
007
74.6
1-0
.31
74.6
274
.94
95.0
01.
007
NM
40.
1104
.70
0.58
104.
7110
6.37
95.2
61.
010
74.8
4-0
.12
74.8
575
.16
95.0
01.
010
NM
40.
2104
.97
0.47
104.
9810
6.63
95.3
21.
013
75.0
9-0
.13
75.0
975
.36
95.2
01.
013
NM
50.
1104
.89
0.69
104.
8910
6.81
95.3
41.
014
74.8
5-0
.32
74.8
675
.46
95.0
41.
014
NM
50.
2105
.54
0.46
105.
5510
7.40
95.2
41.
020
75.2
4-0
.26
75.2
475
.89
94.9
41.
020
NM
60.
1105
.60
0.78
105.
6110
7.24
95.2
01.
019
75.3
20.
0475
.32
75.7
895
.16
1.01
8N
M60.
2106
.80
0.48
106.
8110
8.39
95.3
01.
030
76.1
0-0
.13
76.1
176
.60
95.4
41.
029
NM
70.
1105
.70
1.39
105.
7010
7.67
95.5
41.
023
75.5
00.
1175
.51
76.0
694
.94
1.02
2N
M70.
2107
.91
1.64
107.
9010
9.79
95.4
01.
043
77.1
30.
2377
.14
77.5
594
.90
1.04
2N
M80.
1106
.07
0.68
106.
0810
7.96
95.2
21.
025
76.2
30.
2776
.23
76.3
094
.94
1.02
5N
M80.
2109
.89
0.07
109.
9011
1.47
95.5
01.
059
78.4
90.
3178
.49
78.8
295
.24
1.05
9N
M90.
1106
.45
1.26
106.
4510
8.28
95.3
81.
028
75.8
60.
1875
.87
76.4
995
.24
1.02
8N
M90.
2112
.57
0.97
112.
5811
3.95
95.1
61.
082
79.9
10.
0679
.92
80.5
195
.18
1.08
2
122
Tab
leE
63:
Infe
ren
cefo
rth
e95
thp
erce
nti
leeµ
+1.6
45σ
bas
edon
LN
(µ=
0,σ
2=
1)d
ata
wit
hC
=3.
602
=90
thp
erce
nti
le
Res
ult
sfo
rn
=10
0R
esu
lts
forn
=20
0
RM
SE
Bia
sS
DS
DC
vg.
Rel
.R
MS
EB
ias
SD
SD
Cvg.
Rel
.×
103
×10
3×
103
×10
3%
Len
.×
103×
103
×10
3×
103
%L
en.
CD
795.1
0-1
7.31
794.
9979
2.17
92.8
01.
000
558.
99-8
.76
558.
9756
0.54
93.8
61.
000
MI.
C90
894.7
112
.72
894.
7181
3.36
91.1
21.
027
621.
425.
1862
1.46
568.
4892
.14
1.01
4M
I.C
8095
8.3
712
0.03
950.
9285
2.39
91.8
21.
076
653.
2155
.31
650.
9358
2.69
92.3
21.
040
MI.
D90
202181
2.4
22864
0.33
2021
811.
7432
0046
.09
93.8
240
4.01
156
9.14
19.7
856
8.85
571.
7594
.40
1.02
0M
I.D
80
839.5
871
.98
836.
5783
8.69
93.8
61.
059
574.
0232
.10
573.
1857
7.74
94.7
41.
031
CE
NS
868.6
811
.97
868.
6886
7.27
92.8
21.
095
614.
641.
3961
4.70
608.
4894
.18
1.08
6N
M10.1
795.9
5-1
6.09
795.
8779
3.28
92.9
01.
001
559.
25-8
.57
559.
2456
1.16
93.8
01.
001
NM
10.2
795.9
5-1
6.10
795.
8779
3.31
92.9
01.
001
559.
22-8
.61
559.
2156
1.17
93.7
81.
001
NM
20.1
800.1
6-1
5.93
800.
0879
5.61
92.6
01.
004
561.
20-8
.76
561.
1956
2.73
93.7
81.
004
NM
20.2
800.4
7-1
5.56
800.
4079
5.94
92.6
61.
005
561.
25-8
.98
561.
2456
2.87
93.7
41.
004
NM
30.1
802.5
2-1
7.24
802.
4279
8.68
92.4
81.
008
562.
50-9
.51
562.
4756
4.96
93.8
21.
008
NM
30.2
803.6
0-1
7.45
803.
4979
9.57
92.5
41.
009
562.
97-9
.73
562.
9456
5.59
93.9
21.
009
NM
40.1
803.1
8-1
6.61
803.
0980
2.84
92.5
01.
013
567.
50-5
.63
567.
5356
8.44
93.7
41.
014
NM
40.2
804.5
2-1
7.32
804.
4180
5.13
92.6
21.
016
569.
46-5
.81
569.
4857
0.15
93.4
81.
017
NM
50.1
806.5
2-1
5.56
806.
4580
7.39
92.6
81.
019
571.
16-5
.83
571.
1957
1.44
94.2
81.
019
NM
50.2
812.1
3-1
5.67
812.
0681
2.71
92.6
01.
026
574.
89-5
.06
574.
9357
5.33
94.0
61.
026
NM
60.1
818.3
3-7
.68
818.
3881
3.65
92.8
01.
027
573.
57-6
.55
573.
5957
4.31
93.9
81.
025
NM
60.2
829.0
2-6
.75
829.
0782
4.12
92.5
81.
040
580.
69-6
.96
580.
7158
1.52
93.7
41.
037
NM
70.1
817.3
8-9
.97
817.
4181
7.05
92.8
61.
031
575.
90-7
.72
575.
9057
6.88
93.9
61.
029
NM
70.2
837.0
4-1
0.09
837.
0683
5.26
92.7
61.
054
587.
26-5
.68
587.
2959
0.08
94.1
21.
053
NM
80.1
820.5
9-7
.94
820.
6382
1.07
92.7
21.
036
578.
54-6
.42
578.
5657
9.48
93.9
81.
034
NM
80.2
853.3
8-4
.51
853.
4585
2.00
92.5
81.
076
598.
49-3
.09
598.
5460
1.41
93.9
41.
073
NM
90.1
818.9
8-1
0.23
818.
9982
3.42
92.9
41.
039
583.
83-6
.36
583.
8558
1.54
94.2
21.
037
NM
90.2
858.7
4-7
.94
858.
7987
0.43
93.0
01.
099
619.
14-0
.02
619.
2161
5.71
93.8
41.
098
123
Tab
leE
64:
Infe
ren
cefo
rth
e95
thp
erce
nti
leeµ
+1.6
45σ
bas
edon
LN
(µ=
0,σ
2=
1)d
ata
wit
hC
=3.
602
=90
thp
erce
nti
le
Res
ult
sfo
rn
=10
00R
esu
lts
forn
=20
00
RM
SE
Bia
sS
DS
DC
vg.
Rel
.R
MS
EB
ias
SD
SD
Cvg.
Rel
.×
103
×10
3×
103
×10
3%
Len
.×
103×
103
×10
3×
103
%L
en.
CD
248.
101.
1024
8.12
251.
4495
.10
1.00
017
5.79
-1.4
817
5.80
177.
6295
.22
1.00
0M
I.C
90272.
414.
7527
2.40
252.
9192
.58
1.00
619
2.96
1.25
192.
9717
8.49
92.4
41.
005
MI.
C80
279.
7414
.88
279.
3725
5.10
92.7
41.
015
197.
796.
4319
7.71
179.
6792
.42
1.01
2M
I.D
90249.
495.
5824
9.45
253.
1595
.06
1.00
717
6.98
1.13
176.
9917
8.60
95.3
41.
006
MI.
D80
251.
789.
0025
1.64
254.
4495
.10
1.01
217
7.04
2.35
177.
0417
9.33
95.3
01.
010
CE
NS
268.
916.
0326
8.87
271.
9595
.12
1.08
219
0.25
1.67
190.
2619
1.93
94.9
21.
081
NM
10.1
248.
311.
0324
8.33
251.
7095
.12
1.00
117
5.95
-1.6
517
5.96
177.
7995
.30
1.00
1N
M10
.2248.
351.
0024
8.37
251.
7095
.16
1.00
117
5.96
-1.6
617
5.97
177.
8095
.28
1.00
1N
M20
.1249.
101.
1124
9.12
252.
4295
.08
1.00
417
6.75
-1.2
817
6.76
178.
3195
.18
1.00
4N
M20
.2249.
180.
9324
9.20
252.
4895
.06
1.00
417
6.78
-1.3
217
6.80
178.
3795
.20
1.00
4N
M30
.1249.
961.
7324
9.98
253.
5195
.36
1.00
817
7.65
-1.8
617
7.66
179.
0395
.06
1.00
8N
M30
.2250.
241.
6225
0.26
253.
8095
.42
1.00
917
7.91
-1.7
517
7.92
179.
2495
.02
1.00
9N
M40
.1251.
581.
6225
1.60
254.
7795
.06
1.01
317
8.57
-1.2
217
8.58
179.
9595
.22
1.01
3N
M40
.2252.
401.
3625
2.43
255.
5294
.90
1.01
617
9.19
-1.2
517
9.20
180.
5095
.08
1.01
6N
M50
.1252.
201.
9225
2.22
256.
1495
.08
1.01
917
8.78
-1.7
417
8.79
180.
8895
.02
1.01
8N
M50
.2254.
191.
3725
4.21
257.
7895
.06
1.02
517
9.85
-1.6
017
9.86
182.
0795
.22
1.02
5N
M60
.1254.
232.
1825
4.25
257.
4894
.86
1.02
418
0.28
-0.7
618
0.29
181.
8695
.24
1.02
4N
M60
.2257.
721.
4525
7.74
260.
6895
.20
1.03
718
2.27
-1.1
818
2.29
184.
1495
.18
1.03
7N
M70
.1254.
763.
8825
4.76
258.
8395
.24
1.02
918
0.82
-0.5
818
0.84
182.
7295
.20
1.02
9N
M70
.2261.
084.
5926
1.06
264.
6595
.12
1.05
318
5.35
-0.2
418
5.37
186.
8294
.94
1.05
2N
M80
.1255.
811.
9525
5.83
259.
7394
.96
1.03
318
2.73
-0.1
318
2.75
183.
4894
.72
1.03
3N
M80
.2266.
100.
4826
6.13
269.
2195
.12
1.07
118
8.88
0.04
188.
9019
0.27
95.0
61.
071
NM
90.1
256.
723.
5425
6.72
260.
7295
.00
1.03
718
2.10
-0.3
718
2.11
184.
0895
.16
1.03
6N
M90
.2272.
712.
9027
2.72
275.
5595
.04
1.09
619
2.49
-0.6
219
2.51
194.
5995
.30
1.09
6
124
Tab
leE
65:
Infe
ren
cefo
rth
em
eanµ
bas
edon
N(µ
=0,σ
2=
1)d
ata
wit
hC
=1.
645
=95
thp
erce
nti
le
Res
ult
sfo
rn
=10
0R
esu
lts
forn
=20
0
RM
SE
Bia
sS
DS
DC
vg.
Rel
.R
MS
EB
ias
SD
SD
Cvg.
Rel
.×
103×
103
×10
3×
103
%L
en.
×10
3×
103×
103×
103
%L
en.
CD
101
.30
2.27
101.
2899
.19
94.2
81.
000
70.2
60.
5870
.26
70.5
094
.70
1.00
0M
I.C
90
102
.12
0.47
102.
1398
.96
94.0
80.
998
70.7
6-0
.39
70.7
770
.42
94.6
80.
999
MI.
C80
103
.55
2.77
103.
5299
.41
93.8
21.
002
71.5
30.
8471
.53
70.6
194
.28
1.00
2M
I.D
90
103
.09
2.05
103.
0810
6.03
94.5
41.
069
70.3
00.
5970
.30
70.6
794
.80
1.00
2M
I.D
80
101
.40
2.22
101.
3899
.82
94.4
81.
006
70.2
80.
5670
.29
70.7
294
.70
1.00
3C
EN
S102
.05
3.02
102.
0199
.75
94.1
81.
006
70.4
00.
9370
.40
70.8
394
.66
1.00
5N
M10.
1101
.35
2.29
101.
3399
.23
94.3
21.
000
70.2
50.
6270
.26
70.5
394
.62
1.00
0N
M10.
2101
.33
2.29
101.
3299
.23
94.3
81.
000
70.2
50.
6270
.26
70.5
394
.62
1.00
0N
M20.
1101
.48
2.38
101.
4699
.31
94.4
01.
001
70.3
20.
7470
.32
70.6
094
.64
1.00
1N
M20.
2101
.41
2.40
101.
4099
.33
94.4
01.
001
70.3
70.
7270
.37
70.6
194
.62
1.00
2N
M30.
1101
.61
2.66
101.
5899
.44
94.3
61.
002
70.3
40.
6970
.34
70.6
394
.78
1.00
2N
M30.
2101
.54
2.66
101.
5299
.51
94.5
21.
003
70.4
50.
6670
.46
70.6
894
.84
1.00
2N
M40.
1101
.66
2.63
101.
6499
.48
94.3
01.
003
70.3
10.
7770
.31
70.6
894
.92
1.00
3N
M40.
2101
.70
2.55
101.
6899
.63
94.3
61.
004
70.5
30.
8170
.53
70.8
095
.06
1.00
4N
M50.
1101
.72
2.74
101.
7099
.54
94.4
21.
003
70.3
30.
7870
.33
70.7
094
.78
1.00
3N
M50.
2101
.76
2.74
101.
7399
.85
94.2
61.
007
70.6
20.
8570
.63
70.9
394
.68
1.00
6N
M60.
1101
.75
2.73
101.
7399
.55
94.3
61.
004
70.2
60.
7370
.26
70.7
194
.86
1.00
3N
M60.
2101
.91
2.70
101.
8910
0.08
94.3
41.
009
70.7
70.
7770
.78
71.0
894
.82
1.00
8N
M70.
1101
.74
2.76
101.
7199
.57
94.2
41.
004
70.3
00.
8170
.30
70.7
394
.70
1.00
3N
M70.
2101
.96
2.77
101.
9310
0.38
94.4
41.
012
70.8
20.
9570
.83
71.3
294
.60
1.01
2N
M80.
1101
.84
2.74
101.
8199
.58
94.4
01.
004
70.3
30.
8670
.33
70.7
594
.76
1.00
3N
M80.
2102
.65
2.93
102.
6210
0.76
94.5
01.
016
71.3
51.
0571
.35
71.5
894
.60
1.01
5N
M90.
1101
.88
2.86
101.
8599
.61
94.3
61.
004
70.4
10.
8370
.41
70.7
494
.76
1.00
3N
M90.
2102
.80
3.03
102.
7610
1.19
94.3
61.
020
71.8
61.
1171
.86
71.8
794
.62
1.01
9
125
Tab
leE
66:
Infe
ren
cefo
rth
em
eanµ
bas
edon
N(µ
=0,σ
2=
1)d
ata
wit
hC
=1.
645
=95
thp
erce
nti
le
Res
ult
sfo
rn
=10
00R
esu
lts
forn
=20
00
RM
SE
Bia
sS
DS
DC
vg.
Rel
.R
MS
EB
ias
SD
SD
Cvg.
Rel
.×
103
×10
3×
103×
103
%L
en.
×10
3×
103×
103×
103
%L
en.
CD
31.6
00.
0831
.61
31.6
194
.86
1.00
021
.92
-0.1
421
.92
22.3
595
.44
1.00
0M
I.C
90
31.7
8-0
.09
31.7
931
.61
94.7
21.
000
22.0
4-0
.19
22.0
422
.36
95.3
41.
000
MI.
C80
32.1
40.
0732
.14
31.6
394
.40
1.00
122
.22
0.01
22.2
222
.37
94.8
41.
001
MI.
D90
31.6
10.
0731
.61
31.6
394
.86
1.00
121
.93
-0.1
321
.93
22.3
695
.42
1.00
1M
I.D
80
31.6
00.
0631
.60
31.6
594
.86
1.00
121
.93
-0.1
721
.93
22.3
895
.52
1.00
1C
EN
S31
.69
0.12
31.6
931
.73
94.8
61.
004
21.9
8-0
.07
21.9
922
.44
95.5
01.
004
NM
10.
131
.61
0.07
31.6
131
.62
95.0
01.
000
21.9
2-0
.12
21.9
222
.36
95.4
01.
000
NM
10.
231
.61
0.07
31.6
131
.62
95.0
01.
000
21.9
2-0
.12
21.9
222
.36
95.4
01.
000
NM
20.
131
.63
0.08
31.6
331
.64
94.8
61.
001
21.9
3-0
.16
21.9
322
.37
95.4
81.
001
NM
20.
231
.63
0.08
31.6
431
.64
94.8
21.
001
21.9
4-0
.16
21.9
422
.38
95.5
01.
001
NM
30.
131
.64
0.12
31.6
431
.66
94.7
61.
002
21.9
5-0
.10
21.9
522
.39
95.3
21.
002
NM
30.
231
.66
0.13
31.6
631
.68
94.7
21.
002
21.9
7-0
.10
21.9
722
.40
95.1
41.
002
NM
40.
131
.65
0.11
31.6
531
.67
94.9
81.
002
21.9
6-0
.12
21.9
622
.40
95.4
81.
002
NM
40.
231
.71
0.11
31.7
131
.73
94.9
81.
004
22.0
1-0
.13
22.0
122
.44
95.5
81.
004
NM
50.
131
.70
0.10
31.7
031
.68
94.8
61.
002
21.9
6-0
.09
21.9
622
.41
95.4
81.
002
NM
50.
231
.83
0.10
31.8
331
.78
94.7
01.
006
22.0
2-0
.06
22.0
222
.48
95.3
61.
006
NM
60.
131
.68
0.12
31.6
831
.69
94.8
21.
003
21.9
8-0
.11
21.9
922
.41
95.4
21.
003
NM
60.
231
.85
0.17
31.8
531
.86
94.9
41.
008
22.0
5-0
.08
22.0
522
.53
95.1
41.
008
NM
70.
131
.65
0.09
31.6
531
.69
94.9
01.
003
21.9
4-0
.11
21.9
422
.41
95.4
61.
003
NM
70.
231
.86
0.10
31.8
631
.95
95.0
21.
011
22.0
5-0
.09
22.0
522
.60
95.4
21.
011
NM
80.
131
.70
0.14
31.7
031
.70
94.7
81.
003
21.9
7-0
.06
21.9
822
.42
95.4
01.
003
NM
80.
232
.10
0.16
32.1
032
.07
94.8
81.
015
22.1
60.
0222
.16
22.6
895
.32
1.01
5N
M90.
131
.62
0.11
31.6
331
.70
94.8
41.
003
21.9
7-0
.09
21.9
722
.42
95.5
61.
003
NM
90.
232
.06
0.11
32.0
732
.19
95.1
81.
018
22.2
4-0
.02
22.2
422
.77
95.3
81.
019
126
Tab
leE
67:
Infe
ren
cefo
rth
eva
rian
ceσ
2b
ased
onN
(µ=
0,σ
2=
1)d
ata
wit
hC
=1.
645
=95
thp
erce
nti
le
Res
ult
sfo
rn
=10
0R
esu
lts
forn
=20
0
RM
SE
Bia
sS
DS
DC
vg.
Rel
.R
MS
EB
ias
SD
SD
Cvg.
Rel
.×
103
×10
3×
103
×10
3%
Len
.×
103×
103
×10
3×
103
%L
en.
CD
139.9
8-1
1.13
139.
5513
9.85
93.4
81.
000
98.8
5-3
.48
98.8
099
.65
94.5
01.
000
MI.
C90
150.4
3-1
5.42
149.
6513
9.76
91.5
00.
999
105.
98-5
.82
105.
8399
.68
92.7
21.
000
MI.
C80
155.3
1-7
.17
155.
1614
1.46
91.1
81.
012
109.
23-1
.21
109.
2310
0.41
92.5
21.
008
MI.
D90
510
50.1
716
31.1
651
029.
2124
02.4
394
.90
17.1
7999
.49
0.42
99.5
010
0.43
94.6
81.
008
MI.
D80
146.4
4-0
.72
146.
4514
3.31
94.2
81.
025
99.8
60.
7599
.87
100.
6794
.76
1.01
0C
EN
S14
6.8
7-7
.60
146.
6914
6.37
93.1
81.
047
103.
40-1
.71
103.
4010
4.01
94.4
61.
044
NM
10.1
140.2
6-1
1.02
139.
8414
0.31
93.4
21.
003
99.4
0-3
.25
99.3
510
0.00
94.5
61.
003
NM
10.2
140.2
7-1
1.01
139.
8514
0.33
93.4
21.
003
99.3
7-3
.26
99.3
310
0.01
94.5
21.
004
NM
20.1
141.6
8-1
0.65
141.
3014
1.36
93.1
41.
011
99.9
9-2
.73
99.9
710
0.76
94.5
21.
011
NM
20.2
141.9
2-1
0.57
141.
5414
1.51
93.1
21.
012
100.
03-2
.78
100.
0010
0.86
94.4
61.
012
NM
30.1
142.8
0-9
.31
142.
5114
2.54
93.3
61.
019
100.
48-2
.94
100.
4410
1.43
94.5
21.
018
NM
30.2
143.2
4-9
.27
142.
9514
3.05
93.4
01.
023
100.
85-3
.03
100.
8210
1.78
94.6
21.
021
NM
40.1
143.9
5-9
.41
143.
6514
3.22
93.3
61.
024
100.
93-2
.56
100.
9110
1.96
94.3
21.
023
NM
40.2
145.3
1-9
.67
145.
0114
4.40
93.3
61.
033
101.
79-2
.46
101.
7710
2.84
94.2
41.
032
NM
50.1
144.3
2-8
.89
144.
0614
3.77
93.2
61.
028
101.
71-2
.49
101.
6910
2.29
94.4
81.
026
NM
50.2
146.6
9-8
.88
146.
4314
6.07
93.0
61.
044
103.
53-2
.23
103.
5110
3.95
94.0
61.
043
NM
60.1
144.8
6-8
.93
144.
6014
4.08
93.3
41.
030
102.
10-2
.70
102.
0810
2.48
94.3
21.
028
NM
60.2
148.8
1-9
.04
148.
5514
7.71
93.1
01.
056
104.
99-2
.68
104.
9710
5.09
94.2
21.
055
NM
70.1
144.8
6-8
.84
144.
6014
4.31
93.2
01.
032
101.
97-2
.33
101.
9510
2.67
94.5
61.
030
NM
70.2
150.7
3-8
.70
150.
5014
9.52
92.8
61.
069
105.
81-1
.94
105.
8010
6.42
94.2
41.
068
NM
80.1
144.7
4-8
.91
144.
4814
4.47
93.2
21.
033
102.
05-2
.08
102.
0410
2.81
94.2
41.
032
NM
80.2
151.2
7-8
.32
151.
0615
1.34
93.2
81.
082
107.
12-1
.54
107.
1210
7.70
94.0
81.
081
NM
90.1
145.0
7-8
.38
144.
8414
4.69
92.9
41.
035
102.
21-2
.25
102.
1910
2.88
94.6
81.
032
NM
90.2
153.4
7-7
.89
153.
2815
3.06
93.2
21.
094
108.
08-1
.67
108.
0810
8.86
94.1
41.
092
127
Tab
leE
68:
Infe
ren
cefo
rth
eva
rian
ceσ
2b
ased
onN
(µ=
0,σ
2=
1)d
ata
wit
hC
=1.
645
=95
thp
erce
nti
le
Res
ult
sfo
rn
=10
00R
esu
lts
forn
=20
00
RM
SE
Bia
sS
DS
DC
vg.
Rel
.R
MS
EB
ias
SD
SD
Cvg.
Rel
.×
103
×10
3×
103×
103
%L
en.
×10
3×
103×
103×
103
%L
en.
CD
44.8
3-0
.51
44.8
344
.70
95.0
01.
000
31.6
4-0
.53
31.6
431
.61
94.8
81.
000
MI.
C90
47.6
1-0
.92
47.6
144
.76
93.0
21.
001
33.7
2-0
.56
33.7
231
.66
93.8
41.
002
MI.
C80
48.8
0-0
.23
48.8
144
.88
92.9
01.
004
34.8
60.
1734
.86
31.7
492
.84
1.00
4M
I.D
90
44.9
90.
1445
.00
44.8
494
.84
1.00
331
.64
-0.1
831
.64
31.6
994
.98
1.00
3M
I.D
80
44.9
70.
2544
.98
44.9
195
.06
1.00
531
.82
-0.2
331
.82
31.7
494
.94
1.00
4C
EN
S46
.45
-0.3
246
.45
46.5
494
.96
1.04
133
.06
-0.2
133
.07
32.9
195
.12
1.04
1N
M10.
144
.88
-0.5
544
.88
44.8
494
.78
1.00
331
.72
-0.4
731
.72
31.7
194
.92
1.00
3N
M10.
244
.90
-0.5
644
.90
44.8
594
.78
1.00
331
.73
-0.4
731
.73
31.7
294
.84
1.00
3N
M20.
145
.14
-0.5
245
.14
45.1
694
.90
1.01
031
.92
-0.6
031
.92
31.9
394
.98
1.01
0N
M20.
245
.25
-0.5
145
.25
45.2
194
.90
1.01
131
.97
-0.6
331
.97
31.9
695
.00
1.01
1N
M30.
145
.64
-0.3
345
.64
45.4
894
.58
1.01
732
.15
-0.3
632
.15
32.1
694
.92
1.01
7N
M30.
245
.91
-0.2
645
.91
45.6
494
.62
1.02
132
.27
-0.3
732
.27
32.2
794
.92
1.02
1N
M40.
145
.77
-0.3
645
.78
45.6
994
.74
1.02
232
.30
-0.4
432
.30
32.3
095
.16
1.02
2N
M40.
246
.29
-0.3
646
.29
46.0
894
.82
1.03
132
.57
-0.4
732
.57
32.5
895
.32
1.03
1N
M50.
145
.78
-0.4
145
.78
45.8
395
.06
1.02
532
.47
-0.3
232
.47
32.4
194
.98
1.02
5N
M50.
246
.61
-0.4
046
.61
46.5
694
.82
1.04
232
.98
-0.2
032
.98
32.9
395
.08
1.04
2N
M60.
145
.87
-0.2
945
.87
45.9
394
.82
1.02
732
.55
-0.3
832
.55
32.4
795
.02
1.02
7N
M60.
247
.08
-0.1
447
.08
47.1
194
.72
1.05
433
.57
-0.2
933
.57
33.3
095
.12
1.05
4N
M70.
146
.02
-0.4
546
.02
45.9
894
.82
1.02
932
.53
-0.3
932
.53
32.5
195
.02
1.02
9N
M70.
247
.96
-0.4
147
.96
47.6
594
.68
1.06
633
.72
-0.3
333
.72
33.6
995
.10
1.06
6N
M80.
146
.13
-0.2
346
.13
46.0
494
.78
1.03
032
.72
-0.1
832
.72
32.5
695
.14
1.03
0N
M80.
248
.59
-0.1
048
.60
48.2
294
.96
1.07
934
.46
0.05
34.4
634
.10
94.8
61.
079
NM
90.
146
.00
-0.3
446
.01
46.0
894
.70
1.03
132
.67
-0.3
132
.67
32.5
895
.06
1.03
1N
M90.
248
.97
-0.3
748
.97
48.7
395
.02
1.09
034
.65
-0.1
034
.65
34.4
794
.86
1.09
0
128
Tab
leE
69:
Infe
ren
cefo
rth
e84
thp
erce
nti
leµ
+σ
bas
edon
N(µ
=0,σ
2=
1)d
ata
wit
hC
=1.
645
=95
thp
erce
nti
le
Res
ult
sfo
rn
=10
0R
esu
lts
forn
=20
0
RM
SE
Bia
sS
DS
DC
vg.
Rel
.R
MS
EB
ias
SD
SD
Cvg.
Rel
.×
103×
103
×10
3×
103
%L
en.
×10
3×
103×
103×
103
%L
en.
CD
121.9
9-5
.79
121.
8612
1.49
94.4
61.
000
84.8
4-2
.39
84.8
286
.35
95.8
21.
000
MI.
C90
128.8
8-1
0.58
128.
4612
1.34
92.8
40.
999
89.2
8-4
.93
89.1
686
.34
94.3
21.
000
MI.
C80
133.1
9-4
.76
133.
1212
2.05
92.3
01.
005
92.0
6-1
.69
92.0
586
.68
93.8
01.
004
MI.
D90
223.9
110
.47
223.
6913
4.19
95.2
61.
105
85.0
8-0
.75
85.0
886
.69
95.6
81.
004
MI.
D80
122.2
5-1
.98
122.
2512
2.65
94.9
61.
010
85.2
0-0
.79
85.2
186
.85
95.8
01.
006
CE
NS
126.6
1-3
.51
126.
5712
5.20
94.4
41.
031
87.0
7-1
.26
87.0
788
.86
95.6
01.
029
NM
10.1
122.2
3-5
.73
122.
1112
1.76
94.6
01.
002
85.0
6-2
.25
85.0
486
.55
95.6
41.
002
NM
10.2
122.2
0-5
.71
122.
0812
1.77
94.6
01.
002
85.0
5-2
.25
85.0
386
.56
95.6
61.
002
NM
20.1
123.1
8-5
.50
123.
0712
2.36
94.3
61.
007
85.4
6-1
.89
85.4
586
.99
95.4
01.
007
NM
20.2
123.1
4-5
.45
123.
0312
2.48
94.4
81.
008
85.5
9-1
.93
85.5
887
.06
95.2
81.
008
NM
30.1
123.9
0-4
.59
123.
8312
3.03
94.3
61.
013
85.7
6-2
.05
85.7
487
.38
95.6
81.
012
NM
30.2
123.9
6-4
.57
123.
8912
3.41
94.4
01.
016
86.1
8-2
.13
86.1
687
.65
95.7
21.
015
NM
40.1
124.4
7-4
.70
124.
3912
3.42
94.3
81.
016
85.8
4-1
.79
85.8
387
.69
95.7
61.
016
NM
40.2
125.1
9-4
.96
125.
1112
4.32
94.3
81.
023
86.7
0-1
.72
86.6
988
.34
95.5
21.
023
NM
50.1
124.7
8-4
.34
124.
7112
3.73
94.4
21.
018
86.2
1-1
.76
86.2
187
.87
95.4
81.
018
NM
50.2
125.9
3-4
.43
125.
8712
5.48
94.4
61.
033
87.7
2-1
.61
87.7
189
.13
95.5
01.
032
NM
60.1
125.0
8-4
.40
125.
0212
3.91
94.4
01.
020
86.1
8-1
.93
86.1
687
.99
95.5
01.
019
NM
60.2
127.3
1-4
.62
127.
2412
6.73
94.3
21.
043
88.6
3-1
.96
88.6
290
.01
95.2
21.
042
NM
70.1
125.0
6-4
.32
125.
0012
4.04
94.5
21.
021
86.2
4-1
.66
86.2
488
.10
95.3
41.
020
NM
70.2
128.3
7-4
.46
128.
3012
8.16
94.4
61.
055
89.1
6-1
.42
89.1
591
.05
95.0
41.
054
NM
80.1
125.2
3-4
.37
125.
1712
4.14
94.4
01.
022
86.3
5-1
.49
86.3
588
.17
95.5
81.
021
NM
80.2
129.8
8-4
.12
129.
8212
9.71
94.5
21.
068
90.7
8-1
.15
90.7
992
.14
95.2
41.
067
NM
90.1
125.4
6-4
.00
125.
4112
4.25
94.4
41.
023
86.6
2-1
.61
86.6
288
.22
95.6
01.
022
NM
90.2
131.2
1-3
.89
131.
1613
1.30
94.4
61.
081
92.2
6-1
.19
92.2
693
.25
95.3
01.
080
129
Tab
leE
70:
Infe
ren
cefo
rth
e84
thp
erce
nti
leµ
+σ
bas
edon
N(µ
=0,σ
2=
1)d
ata
wit
hC
=1.
645
=95
thp
erce
nti
le
Res
ult
sfo
rn
=10
00R
esu
lts
forn
=20
00
RM
SE
Bia
sS
DS
DC
vg.
Rel
.R
MS
EB
ias
SD
SD
Cvg.
Rel
.×
103
×10
3×
103×
103
%L
en.
×10
3×
103×
103×
103
%L
en.
CD
38.7
7-0
.43
38.7
738
.71
94.5
81.
000
27.0
8-0
.53
27.0
727
.38
95.4
61.
000
MI.
C90
40.4
1-0
.87
40.4
038
.75
93.7
61.
001
28.2
8-0
.63
28.2
727
.41
94.5
41.
001
MI.
C80
41.6
5-0
.42
41.6
538
.82
92.9
61.
003
29.1
7-0
.10
29.1
827
.46
93.6
61.
003
MI.
D90
38.8
5-0
.17
38.8
538
.79
94.5
21.
002
27.0
9-0
.37
27.0
927
.43
95.3
41.
002
MI.
D80
38.8
1-0
.16
38.8
138
.86
94.6
61.
004
27.1
8-0
.45
27.1
827
.47
95.4
41.
004
CE
NS
39.6
5-0
.31
39.6
639
.79
94.7
81.
028
27.8
4-0
.31
27.8
428
.14
95.5
01.
028
NM
10.
138
.81
-0.4
638
.81
38.8
094
.68
1.00
227
.12
-0.4
827
.12
27.4
495
.54
1.00
2N
M10.
238
.82
-0.4
738
.82
38.8
094
.58
1.00
227
.12
-0.4
827
.12
27.4
495
.46
1.00
2N
M20.
138
.97
-0.4
438
.98
38.9
894
.90
1.00
727
.22
-0.5
927
.22
27.5
795
.42
1.00
7N
M20.
239
.03
-0.4
339
.04
39.0
294
.90
1.00
827
.27
-0.6
027
.26
27.5
995
.58
1.00
8N
M30.
139
.19
-0.3
139
.19
39.1
794
.44
1.01
227
.37
-0.4
127
.37
27.7
095
.54
1.01
2N
M30.
239
.36
-0.2
639
.36
39.2
994
.32
1.01
527
.46
-0.4
227
.46
27.7
895
.66
1.01
5N
M40.
139
.28
-0.3
439
.28
39.2
994
.78
1.01
527
.46
-0.4
727
.46
27.7
995
.52
1.01
5N
M40.
239
.63
-0.3
439
.63
39.5
994
.82
1.02
327
.68
-0.4
927
.68
27.9
995
.44
1.02
3N
M50.
139
.41
-0.3
739
.41
39.3
794
.62
1.01
727
.53
-0.3
927
.53
27.8
595
.54
1.01
7N
M50.
240
.07
-0.3
740
.07
39.9
394
.52
1.03
227
.89
-0.2
927
.89
28.2
495
.64
1.03
2N
M60.
139
.40
-0.2
839
.40
39.4
394
.72
1.01
927
.63
-0.4
327
.63
27.8
895
.60
1.01
9N
M60.
240
.31
-0.1
840
.31
40.3
494
.84
1.04
228
.26
-0.3
728
.26
28.5
395
.06
1.04
2N
M70.
139
.39
-0.4
039
.39
39.4
794
.78
1.02
027
.49
-0.4
327
.49
27.9
195
.80
1.02
0N
M70.
240
.74
-0.4
040
.74
40.7
894
.86
1.05
428
.29
-0.4
028
.29
28.8
495
.80
1.05
4N
M80.
139
.56
-0.2
539
.57
39.5
094
.74
1.02
027
.67
-0.2
927
.67
27.9
395
.66
1.02
0N
M80.
241
.53
-0.1
841
.54
41.2
794
.84
1.06
628
.89
-0.1
028
.89
29.1
995
.58
1.06
6N
M90.
139
.30
-0.3
339
.30
39.5
294
.98
1.02
127
.63
-0.3
827
.63
27.9
595
.50
1.02
1N
M90.
241
.60
-0.3
741
.60
41.7
794
.98
1.07
929
.14
-0.2
129
.14
29.5
495
.46
1.07
9
130
Tab
leE
71:
Infe
ren
cefo
rth
e95
thp
erce
nti
leµ
+1.6
45σ
bas
edon
N(µ
=0,σ
2=
1)d
ata
wit
hC
=1.
645
=95
thp
erce
nti
le
Res
ult
sfo
rn
=10
0R
esu
lts
forn
=20
0
RM
SE
Bia
sS
DS
DC
vg.
Rel
.R
MS
EB
ias
SD
SD
Cvg.
Rel
.×
103
×10
3×
103
×10
3%
Len
.×
103×
103
×10
3×
103
%L
en.
CD
152.
16-1
0.99
151.
7815
2.16
94.5
01.
000
106.
15-4
.30
106.
0710
8.14
95.6
01.
000
MI.
C90
163.
50-1
7.70
162.
5515
2.04
92.5
00.
999
113.
53-7
.86
113.
2710
8.18
93.6
01.
000
MI.
C80
169.
45-9
.62
169.
2015
2.98
91.5
01.
005
117.
50-3
.33
117.
4610
8.65
93.0
01.
005
MI.
D90
347.
3515
.89
347.
0217
1.14
95.4
01.
125
106.
50-1
.62
106.
5010
8.64
95.6
01.
005
MI.
D80
152.
50-4
.68
152.
4415
3.76
94.8
01.
011
106.
75-1
.66
106.
7510
8.87
95.7
01.
007
CE
NS
159.
49-7
.71
159.
3215
8.28
94.4
01.
040
110.
08-2
.68
110.
0611
2.33
95.5
01.
039
NM
10.1
152.
53-1
0.90
152.
1615
2.61
94.5
01.
003
106.
56-4
.10
106.
4910
8.48
95.6
01.
003
NM
10.2
152.
49-1
0.88
152.
1215
2.64
94.5
01.
003
106.
54-4
.10
106.
4810
8.49
95.5
01.
003
NM
20.1
154.
08-1
0.58
153.
7315
3.62
94.4
01.
010
107.
20-3
.58
107.
1510
9.21
95.5
01.
010
NM
20.2
154.
11-1
0.52
153.
7715
3.79
94.3
01.
011
107.
35-3
.63
107.
3010
9.33
95.5
01.
011
NM
30.1
155.
20-9
.26
154.
9415
4.69
94.3
01.
017
107.
70-3
.82
107.
6510
9.87
95.6
01.
016
NM
30.2
155.
41-9
.24
155.
1515
5.29
94.6
01.
021
108.
30-3
.94
108.
2411
0.29
95.6
01.
020
NM
40.1
156.
18-9
.43
155.
9115
5.36
94.3
01.
021
107.
92-3
.44
107.
8811
0.38
95.8
01.
021
NM
40.2
157.
45-9
.81
157.
1615
6.76
94.2
01.
030
109.
16-3
.35
109.
1211
1.40
95.5
01.
030
NM
50.1
156.
63-8
.91
156.
4015
5.85
94.4
01.
024
108.
60-3
.40
108.
5611
0.69
95.5
01.
024
NM
50.2
158.
70-9
.05
158.
4615
8.57
94.4
01.
042
110.
88-3
.20
110.
8511
2.64
95.5
01.
042
NM
60.1
157.
15-8
.99
156.
9115
6.16
94.4
01.
026
108.
68-3
.64
108.
6311
0.89
95.3
01.
025
NM
60.2
160.
99-9
.35
160.
7416
0.50
94.0
01.
055
112.
38-3
.71
112.
3311
4.00
95.2
01.
054
NM
70.1
157.
15-8
.89
156.
9215
6.38
94.3
01.
028
108.
72-3
.26
108.
6811
1.06
95.5
01.
027
NM
70.2
162.
82-9
.12
162.
5816
2.67
94.3
01.
069
113.
23-2
.95
113.
2011
5.56
95.3
01.
069
NM
80.1
157.
30-8
.96
157.
0615
6.54
94.4
01.
029
108.
85-3
.00
108.
8211
1.19
95.4
01.
028
NM
80.2
164.
59-8
.67
164.
3816
4.96
94.5
01.
084
115.
44-2
.58
115.
4211
7.18
95.0
01.
084
NM
90.1
157.
65-8
.42
157.
4415
6.72
94.4
01.
030
109.
22-3
.18
109.
1811
1.27
95.5
01.
029
NM
90.2
166.
79-8
.35
166.
5916
7.24
94.4
01.
099
117.
37-2
.67
117.
3511
8.78
95.0
01.
098
131
Tab
leE
72:
Infe
ren
cefo
rth
e95
thp
erce
nti
leµ
+1.6
45σ
bas
edon
N(µ
=0,σ
2=
1)d
ata
wit
hC
=1.
645
=95
thp
erce
nti
le
Res
ult
sfo
rn
=10
00R
esu
lts
forn
=20
00
RM
SE
Bia
sS
DS
DC
vg.
Rel
.R
MS
EB
ias
SD
SD
Cvg.
Rel
.×
103
×10
3×
103×
103
%L
en.
×10
3×
103×
103×
103
%L
en.
CD
48.6
0-0
.76
48.5
948
.48
94.7
01.
000
34.0
9-0
.78
34.0
834
.29
95.4
01.
000
MI.
C90
51.3
3-1
.38
51.3
248
.55
93.5
01.
001
36.1
1-0
.92
36.1
034
.34
94.0
01.
002
MI.
C80
53.0
8-0
.74
53.0
848
.66
92.9
01.
004
37.4
7-0
.17
37.4
734
.42
92.9
01.
004
MI.
D90
48.7
3-0
.32
48.7
348
.61
94.6
01.
003
34.1
0-0
.52
34.1
034
.37
95.4
01.
002
MI.
D80
48.6
7-0
.30
48.6
848
.71
94.6
01.
005
34.2
5-0
.64
34.2
534
.44
95.2
01.
004
CE
NS
50.1
0-0
.59
50.1
150
.30
95.3
01.
037
35.4
0-0
.46
35.4
035
.57
95.6
01.
037
NM
10.
148
.65
-0.8
048
.65
48.6
394
.80
1.00
334
.16
-0.7
234
.16
34.3
995
.40
1.00
3N
M10.
248
.67
-0.8
148
.67
48.6
394
.70
1.00
334
.17
-0.7
134
.16
34.4
095
.40
1.00
3N
M20.
148
.93
-0.7
748
.93
48.9
494
.80
1.01
034
.34
-0.8
634
.34
34.6
195
.40
1.00
9N
M20.
249
.03
-0.7
649
.03
49.0
094
.60
1.01
134
.41
-0.8
934
.40
34.6
595
.40
1.01
1N
M30.
149
.32
-0.5
849
.32
49.2
594
.70
1.01
634
.59
-0.6
134
.58
34.8
395
.80
1.01
6N
M30.
249
.60
-0.5
149
.60
49.4
494
.70
1.02
034
.72
-0.6
234
.72
34.9
695
.60
1.02
0N
M40.
149
.46
-0.6
249
.46
49.4
695
.00
1.02
034
.73
-0.6
934
.73
34.9
895
.50
1.02
0N
M40.
250
.03
-0.6
350
.03
49.9
294
.80
1.03
035
.07
-0.7
335
.06
35.3
095
.60
1.03
0N
M50.
149
.62
-0.6
749
.62
49.6
094
.60
1.02
334
.87
-0.5
734
.87
35.0
795
.60
1.02
3N
M50.
250
.63
-0.6
750
.63
50.4
694
.70
1.04
135
.44
-0.4
435
.44
35.6
995
.80
1.04
1N
M60.
149
.64
-0.5
549
.64
49.6
995
.00
1.02
535
.01
-0.6
435
.00
35.1
495
.20
1.02
5N
M60.
251
.04
-0.4
051
.05
51.1
095
.20
1.05
436
.04
-0.5
536
.04
36.1
395
.20
1.05
4N
M70.
149
.67
-0.7
249
.67
49.7
594
.80
1.02
634
.83
-0.6
534
.83
35.1
895
.70
1.02
6N
M70.
251
.82
-0.7
251
.82
51.7
694
.90
1.06
836
.12
-0.6
036
.12
36.6
195
.90
1.06
8N
M80.
149
.90
-0.4
949
.90
49.8
195
.10
1.02
735
.10
-0.4
335
.10
35.2
295
.40
1.02
7N
M80.
252
.90
-0.4
152
.90
52.4
995
.20
1.08
337
.02
-0.1
837
.03
37.1
295
.30
1.08
3N
M90.
149
.56
-0.6
149
.56
49.8
494
.90
1.02
835
.04
-0.5
735
.04
35.2
595
.60
1.02
8N
M90.
253
.09
-0.6
853
.09
53.2
095
.00
1.09
737
.36
-0.3
437
.37
37.6
395
.20
1.09
8
132
Tab
leE
73:
Infe
ren
cefo
rµ
+σ
2/2
bas
edon
N(µ
=0,σ
2=
1)d
ata
wit
hC
=1.
645
=95
thp
erce
nti
le
Res
ult
sfo
rn
=10
0R
esu
lts
forn
=20
0
RM
SE
Bia
sS
DS
DC
vg.
Rel
.R
MS
EB
ias
SD
SD
Cvg.
Rel
.×
103
×10
3×
103
×10
3%
Len
.×
103×
103×
103×
103
%L
en.
CD
121.6
9-3
.30
121.
6512
1.43
94.4
01.
000
84.7
7-1
.16
84.7
886
.35
95.8
01.
000
MI.
C90
128.5
6-7
.24
128.
3712
1.30
92.9
00.
999
89.1
9-3
.30
89.1
486
.35
94.3
01.
000
MI.
C80
133.3
4-0
.82
133.
3512
2.27
92.4
01.
007
92.1
30.
2392
.14
86.7
993
.80
1.00
5M
I.D
9025
524.
5581
7.63
2551
4.01
1252
.11
95.4
010
.311
85.1
40.
8185
.15
86.8
095
.70
1.00
5M
I.D
8012
3.4
71.
8612
3.47
123.
3395
.00
1.01
685
.30
0.94
85.3
086
.98
95.8
01.
007
CE
NS
126.5
4-0
.78
126.
5512
5.29
94.4
01.
032
87.0
60.
0887
.07
88.9
395
.60
1.03
0N
M10
.112
1.9
4-3
.22
121.
9112
1.71
94.6
01.
002
84.9
9-1
.01
84.9
986
.56
95.7
01.
002
NM
10.2
121.9
0-3
.21
121.
8712
1.72
94.7
01.
002
84.9
8-1
.01
84.9
986
.57
95.7
01.
002
NM
20.1
122.8
9-2
.94
122.
8712
2.33
94.4
01.
007
85.4
2-0
.63
85.4
287
.01
95.4
01.
008
NM
20.2
122.8
6-2
.89
122.
8312
2.44
94.5
01.
008
85.5
5-0
.67
85.5
687
.09
95.4
01.
008
NM
30.1
123.6
7-2
.00
123.
6612
3.03
94.5
01.
013
85.7
0-0
.78
85.7
187
.41
95.6
01.
012
NM
30.2
123.7
3-1
.97
123.
7312
3.41
94.5
01.
016
86.1
3-0
.85
86.1
487
.67
95.6
01.
015
NM
40.1
124.2
8-2
.07
124.
2812
3.43
94.5
01.
016
85.8
0-0
.51
85.8
087
.72
95.8
01.
016
NM
40.2
125.0
1-2
.29
125.
0012
4.32
94.5
01.
024
86.6
7-0
.42
86.6
888
.38
95.6
01.
023
NM
50.1
124.6
2-1
.70
124.
6312
3.75
94.4
01.
019
86.1
8-0
.47
86.1
987
.91
95.5
01.
018
NM
50.2
125.7
9-1
.70
125.
7912
5.50
94.6
01.
034
87.7
0-0
.26
87.7
189
.17
95.5
01.
033
NM
60.1
124.9
3-1
.74
124.
9312
3.94
94.4
01.
021
86.1
4-0
.62
86.1
588
.03
95.5
01.
019
NM
60.2
127.1
3-1
.82
127.
1312
6.77
94.3
01.
044
88.6
0-0
.57
88.6
190
.05
95.2
01.
043
NM
70.1
124.8
9-1
.66
124.
8912
4.08
94.5
01.
022
86.2
0-0
.36
86.2
088
.14
95.4
01.
021
NM
70.2
128.2
1-1
.58
128.
2212
8.22
94.5
01.
056
89.1
5-0
.02
89.1
691
.11
95.1
01.
055
NM
80.1
125.0
8-1
.71
125.
0812
4.18
94.5
01.
023
86.3
2-0
.18
86.3
388
.22
95.6
01.
022
NM
80.2
129.8
0-1
.23
129.
8012
9.79
94.7
01.
069
90.7
90.
2890
.79
92.2
195
.30
1.06
8N
M90
.112
5.3
4-1
.33
125.
3512
4.30
94.5
01.
024
86.6
0-0
.30
86.6
188
.27
95.6
01.
022
NM
90.2
131.1
9-0
.91
131.
2013
1.41
94.7
01.
082
92.2
90.
2792
.30
93.3
395
.40
1.08
1
133
Tab
leE
74:
Infe
ren
cefo
rµ
+σ
2/2
bas
edon
N(µ
=0,σ
2=
1)d
ata
wit
hC
=1.
645
=95
thp
erce
nti
le
Res
ult
sfo
rn
=10
00R
esu
lts
forn
=20
00
RM
SE
Bia
sS
DS
DC
vg.
Rel
.R
MS
EB
ias
SD
SD
Cvg.
Rel
.×
103
×10
3×
103×
103
%L
en.
×10
3×
103×
103×
103
%L
en.
CD
38.7
7-0
.18
38.7
738
.71
94.5
01.
000
27.0
7-0
.40
27.0
727
.37
95.4
01.
000
MI.
C90
40.4
1-0
.55
40.4
138
.75
93.7
01.
001
28.2
7-0
.47
28.2
727
.41
94.6
01.
001
MI.
C80
41.6
7-0
.04
41.6
738
.83
93.0
01.
003
29.1
80.
1029
.18
27.4
793
.70
1.00
3M
I.D
90
38.8
60.
1438
.86
38.8
094
.50
1.00
227
.10
-0.2
227
.10
27.4
395
.40
1.00
2M
I.D
80
38.8
20.
1838
.83
38.8
794
.60
1.00
427
.18
-0.2
827
.18
27.4
895
.50
1.00
4C
EN
S39
.66
-0.0
439
.66
39.8
094
.70
1.02
827
.84
-0.1
727
.84
28.1
495
.50
1.02
8N
M10.
138
.80
-0.2
138
.81
38.8
094
.70
1.00
227
.12
-0.3
627
.12
27.4
495
.50
1.00
2N
M10.
238
.81
-0.2
138
.82
38.8
094
.60
1.00
227
.12
-0.3
527
.12
27.4
495
.50
1.00
2N
M20.
138
.97
-0.1
838
.97
38.9
994
.90
1.00
727
.22
-0.4
627
.22
27.5
795
.40
1.00
7N
M20.
239
.03
-0.1
739
.03
39.0
294
.90
1.00
827
.26
-0.4
827
.26
27.5
995
.60
1.00
8N
M30.
139
.19
-0.0
539
.20
39.1
794
.40
1.01
227
.37
-0.2
827
.37
27.7
095
.60
1.01
2N
M30.
239
.36
0.00
39.3
739
.30
94.3
01.
015
27.4
6-0
.29
27.4
627
.79
95.6
01.
015
NM
40.
139
.28
-0.0
739
.28
39.3
094
.80
1.01
527
.46
-0.3
427
.46
27.7
995
.60
1.01
5N
M40.
239
.64
-0.0
739
.64
39.5
994
.80
1.02
327
.68
-0.3
627
.68
27.9
995
.50
1.02
3N
M50.
139
.41
-0.1
039
.42
39.3
894
.70
1.01
727
.53
-0.2
527
.53
27.8
595
.50
1.01
7N
M50.
240
.08
-0.1
040
.08
39.9
494
.50
1.03
227
.89
-0.1
627
.89
28.2
495
.60
1.03
2N
M60.
139
.40
-0.0
239
.41
39.4
494
.70
1.01
927
.63
-0.3
027
.63
27.8
895
.60
1.01
9N
M60.
240
.31
0.10
40.3
240
.35
94.8
01.
042
28.2
6-0
.23
28.2
628
.53
95.0
01.
042
NM
70.
139
.39
-0.1
439
.39
39.4
794
.80
1.02
027
.49
-0.3
027
.49
27.9
195
.70
1.02
0N
M70.
240
.74
-0.1
140
.75
40.7
994
.80
1.05
428
.29
-0.2
628
.30
28.8
495
.80
1.05
4N
M80.
139
.57
0.02
39.5
739
.51
94.8
01.
020
27.6
7-0
.15
27.6
727
.94
95.7
01.
020
NM
80.
241
.54
0.11
41.5
441
.28
94.9
01.
066
28.9
00.
0428
.90
29.1
995
.60
1.06
6N
M90.
139
.30
-0.0
639
.31
39.5
395
.00
1.02
127
.63
-0.2
527
.63
27.9
595
.40
1.02
1N
M90.
241
.60
-0.0
741
.61
41.7
794
.90
1.07
929
.13
-0.0
629
.14
29.5
495
.50
1.07
9
134
Tab
leE
75:
Infe
ren
cefo
rth
em
eanµ
bas
edon
N(µ
=0,σ
2=
1)d
ata
wit
hC
=1.
282
=90
thp
erce
nti
le
Res
ult
sfo
rn
=10
0R
esu
lts
forn
=20
0
RM
SE
Bia
sS
DS
DC
vg.
Rel
.R
MS
EB
ias
SD
SD
Cvg.
Rel
.×
103×
103
×10
3×
103
%L
en.
×10
3×
103×
103×
103
%L
en.
CD
98.0
1-1
.17
98.0
199
.14
94.7
21.
000
69.9
7-2
.11
69.9
570
.45
94.8
81.
000
MI.
C90
99.7
5-1
.86
99.7
499
.22
94.4
01.
001
71.4
7-2
.37
71.4
470
.50
94.4
41.
001
MI.
C80
102
.31
3.72
102.
2599
.95
93.7
81.
008
72.3
40.
0272
.35
70.7
994
.42
1.00
5M
I.D
90
98.2
1-1
.14
98.2
299
.74
94.8
81.
006
70.0
2-2
.13
70.0
070
.67
94.9
81.
003
MI.
D80
98.1
8-1
.28
98.1
999
.96
94.9
01.
008
70.0
1-2
.11
69.9
970
.83
94.8
81.
005
CE
NS
98.9
7-0
.26
98.9
810
0.35
94.9
81.
012
70.6
6-1
.76
70.6
471
.21
94.9
61.
011
NM
10.
198.1
3-1
.08
98.1
399
.21
94.5
81.
001
70.0
2-2
.07
70.0
070
.49
94.8
41.
001
NM
10.
298.1
2-1
.09
98.1
399
.21
94.5
61.
001
70.0
4-2
.07
70.0
170
.49
94.8
61.
001
NM
20.
198.1
2-0
.99
98.1
399
.35
94.9
81.
002
70.1
1-2
.09
70.0
870
.57
94.8
21.
002
NM
20.
298.1
5-0
.99
98.1
599
.37
94.9
01.
002
70.1
4-2
.11
70.1
270
.58
94.7
41.
002
NM
30.
198.1
9-0
.95
98.1
999
.50
94.8
61.
004
70.1
4-2
.03
70.1
270
.68
94.9
81.
003
NM
30.
298.1
5-1
.02
98.1
699
.56
94.7
81.
004
70.2
4-1
.95
70.2
270
.73
95.0
01.
004
NM
40.
198.4
0-0
.68
98.4
199
.68
94.7
01.
005
70.2
4-2
.05
70.2
270
.77
94.9
21.
005
NM
40.
298.5
7-0
.73
98.5
899
.84
94.6
21.
007
70.4
3-2
.05
70.4
170
.88
94.8
81.
006
NM
50.
198.6
8-0
.78
98.6
999
.75
94.7
81.
006
70.2
5-2
.19
70.2
270
.80
94.8
41.
005
NM
50.
299.1
1-0
.81
99.1
210
0.09
94.7
41.
010
70.5
0-2
.30
70.4
771
.04
95.0
41.
008
NM
60.
198.5
2-0
.75
98.5
399
.81
94.7
81.
007
70.4
2-1
.80
70.4
170
.91
94.9
41.
007
NM
60.
299.1
9-0
.97
99.1
910
0.42
95.0
01.
013
71.0
0-1
.65
70.9
971
.38
94.7
61.
013
NM
70.
198.8
2-0
.49
98.8
399
.91
94.8
41.
008
70.2
9-1
.96
70.2
770
.92
94.8
81.
007
NM
70.
299.4
2-0
.65
99.4
210
0.92
94.7
61.
018
71.0
3-1
.94
71.0
171
.66
94.9
01.
017
NM
80.
198.5
7-0
.55
98.5
899
.94
94.7
01.
008
70.4
3-1
.93
70.4
170
.95
94.9
61.
007
NM
80.
299.9
3-0
.64
99.9
410
1.45
94.7
41.
023
71.5
4-2
.03
71.5
272
.03
94.8
21.
022
NM
90.
198.4
9-0
.63
98.5
099
.95
94.8
81.
008
70.4
7-1
.84
70.4
570
.98
94.8
61.
008
NM
90.
299.9
2-0
.92
99.9
210
2.05
95.0
81.
029
72.3
2-1
.86
72.3
172
.50
94.6
81.
029
135
Tab
leE
76:
Infe
ren
cefo
rth
em
eanµ
bas
edon
N(µ
=0,σ
2=
1)d
ata
wit
hC
=1.
282
=90
thp
erce
nti
le
Res
ult
sfo
rn
=10
00R
esu
lts
forn
=20
00
RM
SE
Bia
sS
DS
DC
vg.
Rel
.R
MS
EB
ias
SD
SD
Cvg.
Rel
.×
103
×10
3×
103×
103
%L
en.
×10
3×
103×
103×
103
%L
en.
CD
31.4
0-0
.27
31.4
031
.60
95.0
41.
000
22.2
9-0
.02
22.2
922
.34
95.2
01.
000
MI.
C90
31.8
7-0
.22
31.8
731
.63
94.6
21.
001
22.5
9-0
.11
22.5
922
.36
94.6
21.
001
MI.
C80
32.5
20.
2532
.52
31.6
994
.16
1.00
323
.01
0.20
23.0
122
.39
94.3
21.
002
MI.
D90
31.4
2-0
.24
31.4
331
.64
95.2
21.
001
22.3
1-0
.04
22.3
122
.37
94.9
81.
001
MI.
D80
31.5
1-0
.31
31.5
131
.70
95.0
81.
003
22.3
3-0
.02
22.3
422
.41
95.0
01.
003
CE
NS
31.6
9-0
.13
31.6
931
.93
95.0
01.
010
22.5
00.
0322
.50
22.5
794
.88
1.01
0N
M10.
131
.44
-0.2
931
.44
31.6
195
.02
1.00
022
.30
-0.0
322
.30
22.3
695
.10
1.00
0N
M10.
231
.44
-0.2
931
.44
31.6
295
.02
1.00
022
.30
-0.0
322
.30
22.3
695
.10
1.00
1N
M20.
131
.48
-0.2
731
.48
31.6
595
.16
1.00
222
.30
-0.0
222
.31
22.3
895
.10
1.00
2N
M20.
231
.48
-0.2
731
.48
31.6
695
.12
1.00
222
.31
-0.0
222
.31
22.3
995
.04
1.00
2N
M30.
131
.47
-0.2
331
.47
31.7
095
.04
1.00
322
.37
-0.0
122
.37
22.4
295
.28
1.00
3N
M30.
231
.50
-0.2
431
.50
31.7
294
.92
1.00
422
.39
-0.0
322
.40
22.4
395
.24
1.00
4N
M40.
131
.55
-0.2
531
.55
31.7
495
.16
1.00
422
.40
0.03
22.4
122
.44
95.0
61.
004
NM
40.
231
.59
-0.2
331
.59
31.7
995
.00
1.00
622
.43
0.02
22.4
422
.48
95.1
41.
006
NM
50.
131
.58
-0.1
831
.58
31.7
794
.98
1.00
522
.44
0.01
22.4
522
.46
95.0
21.
005
NM
50.
231
.71
-0.1
731
.71
31.8
994
.92
1.00
922
.54
-0.0
122
.55
22.5
495
.00
1.00
9N
M60.
131
.56
-0.2
531
.57
31.7
995
.06
1.00
622
.43
0.00
22.4
322
.48
95.0
21.
006
NM
60.
231
.78
-0.2
531
.78
31.9
995
.06
1.01
222
.54
-0.0
222
.54
22.6
295
.26
1.01
2N
M70.
131
.55
-0.1
731
.55
31.8
195
.24
1.00
722
.44
0.01
22.4
422
.49
95.2
01.
006
NM
70.
231
.87
-0.1
431
.88
32.1
495
.14
1.01
722
.65
-0.0
622
.65
22.7
295
.22
1.01
7N
M80.
131
.55
-0.1
931
.56
31.8
295
.14
1.00
722
.45
0.01
22.4
522
.50
94.9
01.
007
NM
80.
232
.04
-0.0
632
.04
32.3
194
.90
1.02
322
.75
-0.0
822
.75
22.8
495
.42
1.02
2N
M90.
131
.61
-0.1
631
.61
31.8
395
.06
1.00
722
.41
0.03
22.4
122
.50
95.1
01.
007
NM
90.
232
.24
-0.0
332
.25
32.5
295
.00
1.02
922
.83
-0.0
522
.83
22.9
995
.20
1.02
9
136
Tab
leE
77:
Infe
ren
cefo
rth
eva
rian
ceσ
2b
ased
onN
(µ=
0,σ
2=
1)d
ata
wit
hC
=1.
282
=90
thp
erce
nti
le
Res
ult
sfo
rn
=10
0R
esu
lts
forn
=20
0
RM
SE
Bia
sS
DS
DC
vg.
Rel
.R
MS
EB
ias
SD
SD
Cvg.
Rel
.×
103
×10
3×
103
×10
3%
Len
.×
103×
103
×10
3×
103
%L
en.
CD
142.
17-1
1.97
141.
6813
9.73
92.6
81.
000
99.9
8-4
.90
99.8
799
.51
94.2
01.
000
MI.
C90
155.
16-1
0.84
154.
8014
0.92
91.1
21.
009
109.
31-4
.12
109.
2410
0.12
92.2
61.
006
MI.
C80
156.
750.
7315
6.76
143.
5191
.44
1.02
710
9.86
1.25
109.
8610
1.16
92.5
21.
017
MI.
D90
145.
12-2
.03
145.
1214
2.64
93.3
01.
021
100.
80-0
.66
100.
8110
0.53
94.1
01.
010
MI.
D80
144.
17-1
.47
144.
1814
2.86
93.5
21.
022
100.
790.
3910
0.80
100.
8894
.44
1.01
4C
EN
S154.
12-7
.99
153.
9315
2.24
92.9
81.
090
107.
73-3
.31
107.
6910
8.00
94.0
61.
085
NM
10.1
142.
67-1
1.54
142.
2114
0.36
92.7
61.
005
100.
56-4
.70
100.
4699
.94
93.8
41.
004
NM
10.2
142.
64-1
1.56
142.
1814
0.37
92.7
61.
005
100.
55-4
.70
100.
4599
.95
93.8
41.
004
NM
20.1
143.
73-1
1.16
143.
3114
1.82
92.9
41.
015
101.
28-4
.69
101.
1810
0.94
93.9
41.
014
NM
20.2
143.
80-1
1.15
143.
3814
1.90
92.8
81.
016
101.
33-4
.73
101.
2310
0.99
94.1
01.
015
NM
30.1
144.
80-1
0.88
144.
4014
3.49
93.1
21.
027
102.
66-4
.53
102.
5710
2.12
93.9
21.
026
NM
30.2
145.
16-1
1.05
144.
7514
3.77
93.1
01.
029
102.
92-4
.33
102.
8410
2.35
93.9
61.
029
NM
40.1
146.
57-9
.81
146.
2614
5.09
93.0
41.
038
102.
94-4
.49
102.
8510
3.11
93.8
41.
036
NM
40.2
147.
21-9
.92
146.
8914
5.87
93.0
61.
044
103.
38-4
.51
103.
2910
3.68
94.0
41.
042
NM
50.1
148.
10-1
0.19
147.
7614
6.08
92.8
01.
045
104.
19-5
.12
104.
0810
3.77
93.7
81.
043
NM
50.2
149.
44-1
0.30
149.
1014
7.76
93.2
21.
057
105.
36-5
.41
105.
2310
4.96
93.8
01.
055
NM
60.1
149.
12-1
0.06
148.
7914
6.82
93.1
61.
051
104.
17-3
.57
104.
1210
4.47
93.9
01.
050
NM
60.2
151.
85-1
0.64
151.
4914
9.78
93.0
81.
072
106.
21-3
.16
106.
1710
6.70
94.2
01.
072
NM
70.1
148.
79-9
.06
148.
5314
7.51
93.0
41.
056
104.
54-4
.13
104.
4710
4.76
93.9
81.
053
NM
70.2
152.
63-9
.54
152.
3415
2.19
92.9
41.
089
108.
24-3
.92
108.
1810
8.20
94.1
81.
087
NM
80.1
150.
20-9
.27
149.
9214
7.89
93.0
01.
058
104.
24-4
.05
104.
1810
5.06
94.3
21.
056
NM
80.2
156.
29-9
.55
156.
0215
4.48
93.4
81.
106
108.
49-4
.27
108.
4110
9.77
93.9
21.
103
NM
90.1
149.
59-9
.61
149.
3014
8.15
92.9
01.
060
105.
40-3
.61
105.
3510
5.33
94.0
61.
058
NM
90.2
156.
95-1
0.29
156.
6315
6.58
92.6
61.
121
111.
71-3
.66
111.
6611
1.42
94.0
41.
120
137
Tab
leE
78:
Infe
ren
cefo
rth
eva
rian
ceσ
2b
ased
onN
(µ=
0,σ
2=
1)d
ata
wit
hC
=1.
282
=90
thp
erce
nti
le
Res
ult
sfo
rn
=10
00R
esu
lts
forn
=20
00
RM
SE
Bia
sS
DS
DC
vg.
Rel
.R
MS
EB
ias
SD
SD
Cvg.
Rel
.×
103
×10
3×
103×
103
%L
en.
×10
3×
103×
103×
103
%L
en.
CD
44.1
6-0
.92
44.1
544
.68
95.1
21.
000
31.2
1-1
.17
31.1
931
.59
95.1
81.
000
MI.
C90
48.2
1-0
.41
48.2
144
.87
93.4
01.
004
34.1
8-1
.24
34.1
631
.70
92.8
81.
004
MI.
C80
48.8
90.
6948
.89
45.0
992
.94
1.00
934
.48
-0.6
034
.48
31.8
392
.84
1.00
8M
I.D
90
44.4
2-0
.06
44.4
344
.90
95.2
81.
005
31.3
1-0
.84
31.3
031
.72
95.3
21.
004
MI.
D80
44.4
40.
0444
.45
44.9
995
.48
1.00
731
.37
-0.6
731
.37
31.7
895
.44
1.00
6C
EN
S47
.80
-0.3
247
.80
48.4
195
.52
1.08
334
.01
-0.9
434
.00
34.2
095
.12
1.08
3N
M10.
144
.37
-0.9
944
.36
44.8
695
.24
1.00
431
.36
-1.2
031
.34
31.7
295
.18
1.00
4N
M10.
244
.37
-1.0
044
.36
44.8
695
.30
1.00
431
.36
-1.2
031
.34
31.7
295
.18
1.00
4N
M20.
144
.77
-0.9
244
.76
45.3
195
.36
1.01
431
.63
-1.1
731
.61
32.0
395
.22
1.01
4N
M20.
244
.80
-0.9
244
.80
45.3
495
.36
1.01
531
.65
-1.1
831
.63
32.0
595
.22
1.01
5N
M30.
145
.34
-0.7
545
.34
45.8
495
.10
1.02
632
.13
-1.1
432
.12
32.4
095
.18
1.02
6N
M30.
245
.45
-0.7
845
.45
45.9
495
.08
1.02
832
.20
-1.1
832
.18
32.4
795
.18
1.02
8N
M40.
145
.56
-0.8
245
.56
46.2
995
.32
1.03
632
.36
-0.9
232
.35
32.7
395
.04
1.03
6N
M40.
245
.74
-0.7
845
.73
46.5
495
.36
1.04
232
.55
-0.9
632
.54
32.9
194
.86
1.04
2N
M50.
146
.31
-0.5
046
.32
46.6
395
.04
1.04
432
.65
-1.0
332
.64
32.9
595
.20
1.04
3N
M50.
246
.89
-0.4
946
.90
47.1
795
.08
1.05
633
.01
-1.1
032
.99
33.3
495
.06
1.05
5N
M60.
146
.18
-0.8
246
.18
46.8
495
.32
1.04
832
.85
-1.0
632
.83
33.1
195
.04
1.04
8N
M60.
247
.00
-0.8
447
.00
47.8
295
.20
1.07
033
.65
-1.1
333
.64
33.8
194
.88
1.07
0N
M70.
146
.38
-0.5
246
.39
47.0
295
.46
1.05
233
.15
-1.0
233
.14
33.2
395
.10
1.05
2N
M70.
248
.11
-0.4
248
.11
48.5
695
.26
1.08
734
.16
-1.1
934
.14
34.3
194
.88
1.08
6N
M80.
146
.53
-0.5
646
.53
47.1
495
.54
1.05
533
.14
-1.0
233
.12
33.3
195
.18
1.05
5N
M80.
248
.34
-0.2
648
.34
49.2
995
.48
1.10
334
.62
-1.2
934
.60
34.8
294
.88
1.10
2N
M90.
146
.66
-0.4
946
.67
47.2
495
.34
1.05
733
.07
-0.9
333
.06
33.3
995
.18
1.05
7N
M90.
249
.63
-0.1
749
.64
50.0
195
.12
1.11
935
.02
-1.1
035
.01
35.3
394
.72
1.11
9
138
Tab
leE
79:
Infe
ren
cefo
rth
e84
thp
erce
nti
leµ
+σ
bas
edon
N(µ
=0,σ
2=
1)d
ata
wit
hC
=1.
282
=90
thp
erce
nti
le
Res
ult
sfo
rn
=10
0R
esu
lts
forn
=20
0
RM
SE
Bia
sS
DS
DC
vg.
Rel
.R
MS
EB
ias
SD
SD
Cvg.
Rel
.×
103×
103
×10
3×
103
%L
en.
×10
3×
103×
103×
103
%L
en.
CD
121.8
1-9
.72
121.
4312
1.43
94.5
41.
000
85.5
5-5
.82
85.3
686
.28
95.0
81.
000
MI.
C90
131.2
5-1
1.21
130.
7812
1.81
92.9
61.
003
92.8
9-6
.36
92.6
886
.55
92.7
61.
003
MI.
C80
134.7
0-0
.67
134.
7112
3.03
92.5
21.
013
94.2
0-1
.71
94.1
987
.14
92.7
61.
010
MI.
D90
122.3
1-5
.93
122.
1812
2.54
94.7
61.
009
85.8
0-4
.21
85.7
186
.79
95.1
81.
006
MI.
D80
122.4
9-6
.03
122.
3512
2.95
94.8
61.
013
85.7
8-3
.87
85.7
087
.11
95.2
21.
010
CE
NS
128.8
3-7
.23
128.
6412
9.22
94.7
61.
064
90.4
7-4
.87
90.3
591
.64
94.9
41.
062
NM
10.1
122.2
9-9
.44
121.
9312
1.81
94.4
81.
003
85.8
9-5
.70
85.7
186
.55
94.7
41.
003
NM
10.2
122.2
7-9
.46
121.
9212
1.82
94.5
01.
003
85.9
2-5
.69
85.7
486
.55
94.7
21.
003
NM
20.1
122.7
2-9
.20
122.
3912
2.73
94.6
21.
011
86.4
3-5
.73
86.2
587
.18
94.8
81.
010
NM
20.2
122.8
1-9
.18
122.
4812
2.80
94.7
61.
011
86.5
2-5
.77
86.3
487
.23
94.8
61.
011
NM
30.1
123.3
8-9
.05
123.
0612
3.79
94.7
41.
019
87.0
7-5
.62
86.9
087
.93
94.9
41.
019
NM
30.2
123.5
3-9
.22
123.
2012
4.05
94.8
41.
022
87.3
8-5
.45
87.2
288
.13
94.9
41.
021
NM
40.1
124.4
8-8
.30
124.
2212
4.77
94.7
61.
028
87.4
4-5
.62
87.2
788
.57
95.0
41.
026
NM
40.2
125.1
9-8
.43
124.
9212
5.48
94.7
41.
033
88.0
4-5
.65
87.8
689
.08
95.1
01.
032
NM
50.1
125.8
7-8
.65
125.
5912
5.41
94.6
21.
033
88.0
5-6
.12
87.8
489
.00
94.9
01.
032
NM
50.2
127.3
6-8
.79
127.
0712
6.92
94.3
01.
045
89.1
4-6
.40
88.9
290
.07
94.9
61.
044
NM
60.1
125.8
4-8
.59
125.
5612
5.87
94.5
01.
037
88.3
6-4
.95
88.2
389
.41
94.9
61.
036
NM
60.2
128.5
7-9
.20
128.
2512
8.57
94.7
61.
059
90.4
4-4
.65
90.3
391
.38
95.0
81.
059
NM
70.1
126.4
0-7
.81
126.
1712
6.29
94.8
41.
040
88.2
7-5
.40
88.1
189
.61
94.8
01.
039
NM
70.2
129.5
1-8
.37
129.
2513
0.56
94.9
41.
075
91.5
6-5
.38
91.4
192
.70
94.5
81.
074
NM
80.1
126.2
9-8
.02
126.
0512
6.53
94.7
41.
042
88.4
6-5
.32
88.3
189
.80
94.8
41.
041
NM
80.2
131.9
3-8
.49
131.
6713
2.66
94.4
81.
093
92.6
8-5
.64
92.5
294
.17
94.9
01.
091
NM
90.1
125.9
3-8
.26
125.
6712
6.71
94.7
61.
044
89.0
1-5
.04
88.8
889
.96
94.8
21.
043
NM
90.2
132.4
6-9
.19
132.
1613
4.83
94.7
41.
110
95.5
2-5
.26
95.3
995
.77
94.7
21.
110
139
Tab
leE
80:
Infe
ren
cefo
rth
e84
thp
erce
nti
leµ
+σ
bas
edon
N(µ
=0,σ
2=
1)d
ata
wit
hC
=1.
282
=90
thp
erce
nti
le
Res
ult
sfo
rn
=10
00R
esu
lts
forn
=20
00
RM
SE
Bia
sS
DS
DC
vg.
Rel
.R
MS
EB
ias
SD
SD
Cvg.
Rel
.×
103
×10
3×
103×
103
%L
en.
×10
3×
103×
103×
103
%L
en.
CD
38.3
9-0
.98
38.3
838
.70
95.3
21.
000
27.2
8-0
.73
27.2
727
.37
95.2
01.
000
MI.
C90
41.2
1-0
.80
41.2
138
.82
93.3
21.
003
29.2
7-0
.92
29.2
527
.44
93.5
61.
003
MI.
C80
42.5
50.
1342
.56
39.0
092
.80
1.00
830
.06
-0.3
330
.06
27.5
692
.90
1.00
7M
I.D
90
38.5
6-0
.61
38.5
638
.85
95.3
61.
004
27.3
6-0
.62
27.3
627
.47
95.1
61.
004
MI.
D80
38.7
1-0
.67
38.7
138
.98
95.2
01.
007
27.4
2-0
.54
27.4
227
.56
95.2
01.
007
CE
NS
40.6
5-0
.58
40.6
541
.08
95.1
81.
061
28.9
8-0
.58
28.9
829
.04
95.1
41.
061
NM
10.
138
.59
-1.0
338
.58
38.8
295
.34
1.00
327
.37
-0.7
527
.36
27.4
595
.22
1.00
3N
M10.
238
.59
-1.0
438
.58
38.8
295
.30
1.00
327
.37
-0.7
527
.36
27.4
595
.18
1.00
3N
M20.
138
.85
-0.9
838
.84
39.1
095
.42
1.01
027
.49
-0.7
327
.49
27.6
595
.26
1.01
0N
M20.
238
.87
-0.9
838
.86
39.1
395
.40
1.01
127
.51
-0.7
427
.51
27.6
795
.24
1.01
1N
M30.
139
.08
-0.8
739
.07
39.4
495
.30
1.01
927
.86
-0.7
127
.85
27.8
995
.18
1.01
9N
M30.
239
.18
-0.8
939
.17
39.5
395
.30
1.02
127
.94
-0.7
527
.94
27.9
595
.14
1.02
1N
M40.
139
.36
-0.9
239
.36
39.7
395
.14
1.02
628
.04
-0.5
628
.04
28.0
994
.78
1.02
7N
M40.
239
.52
-0.8
839
.51
39.9
695
.18
1.03
228
.20
-0.5
928
.19
28.2
594
.92
1.03
2N
M50.
139
.74
-0.6
939
.74
39.9
494
.96
1.03
228
.28
-0.6
428
.28
28.2
494
.60
1.03
2N
M50.
240
.28
-0.6
940
.28
40.4
394
.96
1.04
528
.64
-0.7
028
.64
28.5
894
.72
1.04
4N
M60.
139
.67
-0.9
239
.66
40.0
895
.12
1.03
628
.31
-0.6
628
.31
28.3
495
.00
1.03
6N
M60.
240
.50
-0.9
540
.49
40.9
695
.02
1.05
828
.92
-0.7
328
.91
28.9
695
.04
1.05
8N
M70.
139
.69
-0.7
039
.69
40.1
995
.42
1.03
828
.48
-0.6
428
.47
28.4
295
.02
1.03
8N
M70.
241
.16
-0.6
441
.16
41.5
895
.28
1.07
429
.37
-0.8
029
.36
29.3
994
.80
1.07
4N
M80.
139
.78
-0.7
439
.78
40.2
795
.26
1.04
128
.49
-0.6
328
.48
28.4
795
.06
1.04
0N
M80.
241
.57
-0.4
841
.58
42.2
695
.00
1.09
229
.78
-0.8
829
.77
29.8
794
.90
1.09
1N
M90.
139
.97
-0.6
839
.97
40.3
495
.32
1.04
228
.37
-0.5
728
.37
28.5
295
.06
1.04
2N
M90.
242
.61
-0.4
342
.61
42.9
795
.30
1.11
030
.11
-0.7
530
.10
30.3
895
.18
1.11
0
140
Tab
leE
81:
Infe
ren
cefo
rth
e95
thp
erce
nti
leµ
+1.6
45σ
bas
edon
N(µ
=0,σ
2=
1)d
ata
wit
hC
=1.
282
=90
thp
erce
nti
le
Res
ult
sfo
rn
=10
0R
esu
lts
forn
=20
0
RM
SE
Bia
sS
DS
DC
vg.
Rel
.R
MS
EB
ias
SD
SD
Cvg.
Rel
.×
103
×10
3×
103
×10
3%
Len
.×
103×
103
×10
3×
103
%L
en.
CD
153.
85-1
5.24
153.
1115
2.08
93.9
01.
000
107.
48-8
.21
107.
1810
8.06
94.7
01.
000
MI.
C90
168.
45-1
7.25
167.
5815
2.68
92.0
01.
004
118.
68-8
.94
118.
3510
8.48
92.3
01.
004
MI.
C80
171.
95-3
.51
171.
9315
4.29
91.7
01.
015
120.
05-2
.82
120.
0310
9.28
92.2
01.
011
MI.
D90
154.
48-9
.02
154.
2415
3.62
94.1
01.
010
107.
90-5
.56
107.
7710
8.78
94.7
01.
007
MI.
D80
154.
80-9
.10
154.
5515
4.12
94.3
01.
013
107.
85-5
.01
107.
7510
9.20
95.0
01.
010
CE
NS
165.
22-1
1.73
164.
8216
4.68
94.2
01.
083
115.
48-6
.88
115.
2811
6.77
94.6
01.
081
NM
10.1
154.
53-1
4.84
153.
8315
2.71
93.9
01.
004
108.
05-8
.04
107.
7610
8.50
94.4
01.
004
NM
10.2
154.
51-1
4.85
153.
8115
2.72
93.9
01.
004
108.
08-8
.03
107.
7910
8.51
94.4
01.
004
NM
20.1
155.
33-1
4.49
154.
6715
4.19
93.9
01.
014
108.
90-8
.07
108.
6110
9.54
94.7
01.
014
NM
20.2
155.
45-1
4.47
154.
7915
4.30
93.9
01.
015
109.
02-8
.13
108.
7210
9.61
94.6
01.
014
NM
30.1
156.
44-1
4.28
155.
8115
5.92
94.3
01.
025
110.
05-7
.94
109.
7711
0.76
94.5
01.
025
NM
30.2
156.
76-1
4.52
156.
1015
6.31
94.2
01.
028
110.
47-7
.70
110.
2111
1.05
94.6
01.
028
NM
40.1
158.
15-1
3.22
157.
6115
7.50
94.2
01.
036
110.
56-7
.93
110.
2911
1.80
94.9
01.
035
NM
40.2
159.
16-1
3.40
158.
6115
8.55
94.4
01.
043
111.
37-7
.97
111.
1011
2.55
94.9
01.
042
NM
50.1
160.
22-1
3.73
159.
6515
8.55
94.0
01.
042
111.
68-8
.65
111.
3611
2.51
94.5
01.
041
NM
50.2
162.
33-1
3.94
161.
7416
0.79
93.8
01.
057
113.
30-9
.05
112.
9511
4.10
94.8
01.
056
NM
60.1
160.
45-1
3.64
159.
8815
9.30
94.3
01.
047
111.
97-6
.98
111.
7711
3.15
94.5
01.
047
NM
60.2
164.
43-1
4.52
163.
8016
3.28
94.1
01.
074
114.
94-6
.58
114.
7611
6.07
94.9
01.
074
NM
70.1
160.
96-1
2.53
160.
4915
9.94
94.2
01.
052
112.
02-7
.62
111.
7711
3.49
94.7
01.
050
NM
70.2
165.
74-1
3.35
165.
2216
6.23
94.3
01.
093
116.
89-7
.59
116.
6611
8.03
94.4
01.
092
NM
80.1
161.
22-1
2.84
160.
7316
0.35
94.3
01.
054
112.
13-7
.51
111.
8911
3.79
94.8
01.
053
NM
80.2
169.
49-1
3.55
168.
9616
9.28
94.5
01.
113
118.
21-7
.97
117.
9512
0.16
94.8
01.
112
NM
90.1
160.
68-1
3.18
160.
1516
0.64
94.2
01.
056
113.
10-7
.11
112.
8911
4.05
94.7
01.
055
NM
90.2
170.
41-1
4.52
169.
8117
2.36
94.4
01.
133
122.
31-7
.45
122.
1012
2.44
94.5
01.
133
141
Tab
leE
82:
Infe
ren
cefo
rth
e95
thp
erce
nti
leµ
+1.6
45σ
bas
edon
N(µ
=0,σ
2=
1)d
ata
wit
hC
=1.
282
=90
thp
erce
nti
le
Res
ult
sfo
rn
=10
00R
esu
lts
forn
=20
00
RM
SE
Bia
sS
DS
DC
vg.
Rel
.R
MS
EB
ias
SD
SD
Cvg.
Rel
.×
103
×10
3×
103×
103
%L
en.
×10
3×
103×
103×
103
%L
en.
CD
48.0
3-1
.43
48.0
148
.47
95.5
01.
000
34.1
0-1
.19
34.0
834
.28
95.3
01.
000
MI.
C90
52.5
0-1
.18
52.4
948
.66
92.8
01.
004
37.2
9-1
.44
37.2
634
.40
93.0
01.
004
MI.
C80
54.1
30.
0554
.13
48.9
192
.60
1.00
938
.21
-0.6
738
.21
34.5
792
.60
1.00
8M
I.D
90
48.3
0-0
.85
48.2
948
.70
95.5
01.
005
34.2
2-1
.00
34.2
134
.43
95.5
01.
004
MI.
D80
48.4
6-0
.90
48.4
648
.86
95.4
01.
008
34.3
0-0
.88
34.3
034
.54
95.4
01.
008
CE
NS
51.7
4-0
.86
51.7
452
.34
95.0
01.
080
36.9
1-0
.98
36.9
037
.00
95.1
01.
079
NM
10.
148
.32
-1.5
148
.30
48.6
695
.40
1.00
434
.25
-1.2
234
.23
34.4
195
.20
1.00
4N
M10.
248
.32
-1.5
248
.30
48.6
795
.30
1.00
434
.25
-1.2
134
.23
34.4
195
.20
1.00
4N
M20.
148
.75
-1.4
448
.73
49.1
395
.40
1.01
434
.47
-1.1
834
.46
34.7
495
.40
1.01
4N
M20.
248
.78
-1.4
448
.77
49.1
795
.40
1.01
434
.50
-1.2
034
.49
34.7
795
.40
1.01
4N
M30.
149
.19
-1.2
849
.18
49.6
895
.30
1.02
535
.05
-1.1
635
.03
35.1
395
.50
1.02
5N
M30.
249
.34
-1.3
149
.32
49.8
195
.20
1.02
835
.17
-1.2
135
.15
35.2
295
.40
1.02
7N
M40.
149
.59
-1.3
649
.57
50.1
595
.00
1.03
535
.33
-0.9
435
.32
35.4
694
.90
1.03
5N
M40.
249
.81
-1.3
049
.80
50.4
995
.10
1.04
235
.56
-0.9
835
.55
35.7
094
.90
1.04
2N
M50.
150
.24
-1.0
350
.24
50.5
095
.20
1.04
235
.69
-1.0
635
.68
35.7
094
.90
1.04
2N
M50.
251
.03
-1.0
351
.03
51.2
295
.20
1.05
736
.21
-1.1
436
.20
36.2
195
.00
1.05
6N
M60.
150
.13
-1.3
650
.12
50.7
295
.20
1.04
635
.79
-1.0
935
.78
35.8
795
.00
1.04
6N
M60.
251
.32
-1.4
051
.30
52.0
295
.10
1.07
336
.72
-1.1
936
.71
36.7
894
.90
1.07
3N
M70.
150
.21
-1.0
450
.20
50.9
095
.30
1.05
036
.07
-1.0
636
.06
35.9
995
.20
1.05
0N
M70.
252
.40
-0.9
652
.40
52.9
595
.20
1.09
237
.39
-1.2
837
.37
37.4
395
.10
1.09
2N
M80.
150
.35
-1.0
950
.35
51.0
395
.20
1.05
336
.08
-1.0
536
.06
36.0
895
.00
1.05
3N
M80.
252
.93
-0.7
552
.93
53.9
395
.00
1.11
337
.99
-1.3
937
.97
38.1
195
.00
1.11
2N
M90.
150
.61
-1.0
250
.61
51.1
495
.30
1.05
535
.93
-0.9
535
.92
36.1
595
.20
1.05
5N
M90.
254
.49
-0.6
854
.49
54.9
595
.20
1.13
438
.48
-1.2
138
.47
38.8
495
.30
1.13
3
142
Tab
leE
83:
Infe
ren
cefo
rµ
+σ
2/2
bas
edon
N(µ
=0,σ
2=
1)d
ata
wit
hC
=1.
282
=90
thp
erce
nti
le
Res
ult
sfo
rn
=10
0R
esu
lts
forn
=20
0
RM
SE
Bia
sS
DS
DC
vg.
Rel
.R
MS
EB
ias
SD
SD
Cvg.
Rel
.×
103×
103
×10
3×
103
%L
en.
×10
3×
103×
103×
103
%L
en.
CD
121
.43
-7.1
512
1.23
121.
3694
.50
1.00
085
.40
-4.5
685
.28
86.2
795
.00
1.00
0M
I.C
90
131
.10
-7.2
813
0.91
121.
9593
.10
1.00
592
.81
-4.4
392
.71
86.6
192
.80
1.00
4M
I.C
80
135
.17
4.09
135.
1312
3.55
92.6
01.
018
94.2
90.
6594
.30
87.3
392
.80
1.01
2M
I.D
90
122
.75
-2.1
612
2.75
122.
9794
.90
1.01
385
.79
-2.4
685
.76
86.9
095
.20
1.00
7M
I.D
80
122
.62
-2.0
112
2.61
123.
3494
.90
1.01
685
.79
-1.9
185
.78
87.2
695
.30
1.01
1C
EN
S128
.91
-4.2
512
8.85
129.
3794
.70
1.06
690
.39
-3.4
290
.34
91.7
095
.00
1.06
3N
M10.
1121
.92
-6.8
612
1.74
121.
7594
.50
1.00
385
.75
-4.4
385
.64
86.5
494
.70
1.00
3N
M10.
2121
.90
-6.8
712
1.72
121.
7694
.60
1.00
385
.77
-4.4
285
.67
86.5
594
.70
1.00
3N
M20.
1122
.41
-6.5
712
2.25
122.
6894
.70
1.01
186
.29
-4.4
486
.19
87.1
894
.90
1.01
0N
M20.
2122
.50
-6.5
612
2.33
122.
7594
.90
1.01
186
.38
-4.4
786
.28
87.2
295
.00
1.01
1N
M30.
1123
.05
-6.3
912
2.90
123.
7594
.80
1.02
086
.95
-4.3
086
.85
87.9
394
.90
1.01
9N
M30.
2123
.19
-6.5
512
3.03
124.
0194
.90
1.02
287
.26
-4.1
187
.18
88.1
395
.00
1.02
2N
M40.
1124
.27
-5.5
912
4.16
124.
7794
.70
1.02
887
.31
-4.2
987
.21
88.5
795
.10
1.02
7N
M40.
2124
.95
-5.6
912
4.84
125.
4794
.70
1.03
487
.91
-4.3
187
.81
89.0
895
.10
1.03
3N
M50.
1125
.62
-5.8
812
5.50
125.
4294
.70
1.03
387
.89
-4.7
587
.77
89.0
094
.90
1.03
2N
M50.
2127
.07
-5.9
612
6.95
126.
9294
.50
1.04
688
.98
-5.0
088
.85
90.0
794
.90
1.04
4N
M60.
1125
.68
-5.7
812
5.56
125.
9094
.60
1.03
788
.26
-3.5
988
.19
89.4
494
.90
1.03
7N
M60.
2128
.35
-6.2
912
8.21
128.
5694
.80
1.05
990
.35
-3.2
390
.30
91.4
295
.20
1.06
0N
M70.
1126
.25
-5.0
212
6.16
126.
3494
.90
1.04
188
.14
-4.0
388
.05
89.6
494
.80
1.03
9N
M70.
2129
.29
-5.4
212
9.19
130.
5994
.90
1.07
691
.43
-3.9
091
.36
92.7
394
.70
1.07
5N
M80.
1126
.23
-5.1
812
6.14
126.
5994
.80
1.04
388
.34
-3.9
688
.26
89.8
394
.90
1.04
1N
M80.
2131
.81
-5.4
113
1.71
132.
7194
.50
1.09
492
.57
-4.1
692
.49
94.1
994
.90
1.09
2N
M90.
1125
.77
-5.4
412
5.67
126.
7694
.60
1.04
588
.93
-3.6
588
.86
90.0
094
.80
1.04
3N
M90.
2132
.20
-6.0
713
2.07
134.
8694
.80
1.11
195
.46
-3.6
995
.39
95.8
294
.70
1.11
1
143
Tab
leE
84:
Infe
ren
cefo
rµ
+σ
2/2
bas
edon
N(µ
=0,σ
2=
1)d
ata
wit
hC
=1.
282
=90
thp
erce
nti
le
Res
ult
sfo
rn
=10
00R
esu
lts
forn
=20
00
RM
SE
Bia
sS
DS
DC
vg.
Rel
.R
MS
EB
ias
SD
SD
Cvg.
Rel
.×
103
×10
3×
103×
103
%L
en.
×10
3×
103×
103×
103
%L
en.
CD
38.3
8-0
.73
38.3
738
.70
95.3
01.
000
27.2
7-0
.61
27.2
627
.36
95.2
01.
000
MI.
C90
41.2
1-0
.43
41.2
138
.83
93.4
01.
003
29.2
5-0
.73
29.2
527
.44
93.6
01.
003
MI.
C80
42.5
70.
6042
.57
39.0
292
.80
1.00
830
.05
-0.1
030
.05
27.5
692
.90
1.00
7M
I.D
90
38.5
6-0
.27
38.5
638
.86
95.4
01.
004
27.3
5-0
.46
27.3
527
.47
95.1
01.
004
MI.
D80
38.7
1-0
.29
38.7
138
.99
95.2
01.
008
27.4
2-0
.35
27.4
227
.56
95.2
01.
007
CE
NS
40.6
5-0
.29
40.6
541
.08
95.2
01.
062
28.9
7-0
.44
28.9
729
.04
95.1
01.
061
NM
10.
138
.57
-0.7
838
.57
38.8
295
.40
1.00
327
.35
-0.6
327
.35
27.4
595
.20
1.00
3N
M10.
238
.57
-0.7
938
.57
38.8
295
.30
1.00
327
.35
-0.6
327
.35
27.4
595
.20
1.00
3N
M20.
138
.83
-0.7
338
.83
39.1
095
.40
1.01
027
.48
-0.6
027
.48
27.6
595
.20
1.01
0N
M20.
238
.85
-0.7
338
.85
39.1
395
.50
1.01
127
.50
-0.6
127
.50
27.6
695
.30
1.01
1N
M30.
139
.07
-0.6
139
.07
39.4
495
.30
1.01
927
.85
-0.5
827
.84
27.8
895
.20
1.01
9N
M30.
239
.17
-0.6
339
.17
39.5
395
.30
1.02
127
.93
-0.6
227
.93
27.9
495
.10
1.02
1N
M40.
139
.35
-0.6
639
.35
39.7
395
.20
1.02
728
.04
-0.4
328
.04
28.0
994
.80
1.02
7N
M40.
239
.50
-0.6
239
.50
39.9
695
.20
1.03
228
.19
-0.4
628
.19
28.2
594
.90
1.03
2N
M50.
139
.74
-0.4
339
.74
39.9
594
.90
1.03
228
.27
-0.5
028
.27
28.2
494
.60
1.03
2N
M50.
240
.28
-0.4
240
.28
40.4
395
.00
1.04
528
.63
-0.5
628
.62
28.5
894
.70
1.04
4N
M60.
139
.66
-0.6
639
.66
40.0
895
.10
1.03
628
.30
-0.5
328
.30
28.3
495
.00
1.03
6N
M60.
240
.49
-0.6
740
.49
40.9
695
.00
1.05
828
.90
-0.5
928
.90
28.9
695
.10
1.05
8N
M70.
139
.69
-0.4
339
.70
40.2
095
.40
1.03
928
.47
-0.5
028
.47
28.4
195
.10
1.03
8N
M70.
241
.16
-0.3
541
.17
41.5
995
.30
1.07
529
.36
-0.6
629
.36
29.3
994
.80
1.07
4N
M80.
139
.77
-0.4
639
.77
40.2
895
.20
1.04
128
.48
-0.4
928
.48
28.4
795
.10
1.04
0N
M80.
241
.57
-0.1
941
.57
42.2
695
.00
1.09
229
.77
-0.7
329
.76
29.8
694
.90
1.09
1N
M90.
139
.96
-0.4
139
.97
40.3
495
.40
1.04
228
.36
-0.4
328
.36
28.5
295
.10
1.04
2N
M90.
242
.61
-0.1
242
.62
42.9
895
.20
1.11
130
.09
-0.6
030
.09
30.3
795
.20
1.11
0
144
APPENDIX F: ANALYSIS OF FULLY MASKED DATA ON TOTAL HOUSEHOLD INCOMEAND HOUSEHOLD ALIMONEY PAYEMENT BASED ON DATA FROM THE 2000 U.S.
CURRENT POPULATION SURVEY
In this appendix we present tables summarizing analysis of two variables of the 2000 U.S.Current Population Survey data under full data masking. The data and notations appearing in thetables are described in Section 7 of the paper.
Table F1. Analysis of household total income under full masking
µ σ2 eµ+σ2/2 e2µ+2σ2 − e2µ+σ2eµ+σ eµ+1.645σ
Est Rel. Est Rel. Est Rel. Est× 10−6 Rel. Est Rel. Est Rel.Len. Len. Len. Len. Len. Len.
CD 10.495 1.000 0.981 1.000 58996 1.000 5805.083 1.000 97263 1.000 184262 1.000MI 10.495 1.015 0.980 1.013 58977 1.016 5793.485 1.014 97231 1.016 184145 1.015NM10U 10.494 1.001 0.980 1.003 58958 1.001 5790.372 1.000 97201 1.001 184097 1.001NM10C 10.494 1.002 0.981 1.003 58962 1.001 5795.846 1.001 97207 1.002 184139 1.002NM20U 10.495 1.008 0.983 1.015 59041 1.011 5827.769 1.017 97338 1.011 184492 1.013NM20C 10.496 1.006 0.980 1.012 59048 1.009 5804.365 1.011 97349 1.009 184354 1.011NM30U 10.493 1.015 0.980 1.028 58879 1.017 5769.845 1.019 97071 1.018 183817 1.021NM30C 10.493 1.016 0.984 1.033 59003 1.022 5833.608 1.033 97277 1.022 184462 1.026NM40U 10.493 1.032 0.987 1.059 59074 1.042 5872.531 1.063 97394 1.041 184845 1.049NM40C 10.493 1.027 0.982 1.054 58932 1.035 5803.355 1.047 97159 1.035 184134 1.041NM50U 10.495 1.048 0.983 1.087 59057 1.061 5829.819 1.082 97364 1.061 184535 1.071NM50C 10.494 1.038 0.978 1.078 58889 1.050 5755.189 1.061 97086 1.051 183738 1.060NM60U 10.489 1.076 0.990 1.139 58936 1.093 5878.810 1.134 97168 1.092 184631 1.109NM60C 10.493 1.056 0.980 1.115 58892 1.074 5775.893 1.096 97092 1.074 183881 1.088NM70U 10.485 1.108 0.991 1.201 58741 1.127 5848.492 1.179 96847 1.126 184076 1.150NM70C 10.497 1.075 0.983 1.156 59196 1.106 5861.327 1.148 97595 1.106 184997 1.126NM80U 10.483 1.149 0.984 1.277 58404 1.160 5710.635 1.210 96288 1.160 182554 1.191NM80C 10.492 1.095 0.984 1.200 58919 1.129 5812.647 1.177 97138 1.129 184171 1.155NM90U 10.481 1.198 0.951 1.367 57307 1.165 5216.701 1.163 94454 1.173 177174 1.205NM90C 10.490 1.113 0.977 1.239 58616 1.149 5691.716 1.189 96635 1.150 182819 1.180
145
Table F2. Analysis of household alimony payments under full masking
µ σ2 eµ+σ2/2 e2µ+2σ2 − e2µ+σ2eµ+σ eµ+1.645σ
Est Rel. Est Rel. Est Rel. Est× 10−6 Rel. Est Rel. Est Rel.Len. Len. Len. Len. Len. Len.
CD 8.715 1.000 1.168 1.000 10930 1.000 264.812 1.000 17962 1.000 36069 1.000MI 8.724 1.004 1.147 1.012 10988 1.037 280.919 1.329 18013 1.027 36058 1.039NM10U 8.709 1.000 1.165 1.000 10847 0.993 259.675 0.981 17828 0.993 35767 0.993NM10C 8.715 1.003 1.172 1.006 10947 1.006 267.222 1.014 17987 1.005 36164 1.007NM20U 8.724 1.013 1.185 1.026 11115 1.035 280.355 1.079 18255 1.031 36834 1.037NM20C 8.707 1.006 1.169 1.012 10843 1.000 260.912 0.996 17818 1.000 35788 1.001NM30U 8.720 1.035 1.220 1.071 11272 1.081 303.136 1.204 18484 1.069 37683 1.089NM30C 8.702 1.005 1.151 1.011 10695 0.986 247.352 0.946 17587 0.989 35136 0.987NM40U 8.709 1.011 1.135 1.021 10690 0.991 241.386 0.934 17587 0.997 34968 0.993NM40C 8.712 1.028 1.182 1.057 10977 1.043 272.638 1.078 18030 1.039 36358 1.049NM50U 8.705 1.027 1.137 1.053 10650 1.008 240.305 0.955 17520 1.013 34857 1.013NM50C 8.738 1.025 1.147 1.050 11058 1.046 262.552 1.040 18185 1.049 36280 1.051NM60U 8.737 1.099 1.266 1.207 11733 1.219 350.650 1.533 19194 1.192 39661 1.242NM60C 8.704 1.020 1.102 1.040 10458 0.983 219.756 0.872 17220 0.994 33890 0.986NM70U 8.688 1.100 1.197 1.203 10795 1.112 269.324 1.183 17719 1.102 35888 1.133NM70C 8.712 1.063 1.168 1.129 10896 1.084 262.985 1.107 17906 1.082 35951 1.098NM80U 8.667 1.168 1.273 1.345 10981 1.214 310.293 1.475 17956 1.183 37181 1.249NM80C 8.735 1.058 1.116 1.120 10863 1.075 242.053 1.024 17881 1.084 35339 1.088NM90U 8.694 1.230 1.294 1.491 11397 1.331 343.876 1.762 18614 1.287 38769 1.383NM90C 8.738 1.141 1.282 1.302 11842 1.303 365.256 1.710 19354 1.267 40176 1.337
146