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7/24/2019 10.DISTRIBUCIONES TEORICAS
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PRUEBA DE CHI CUADRADO
m P P(ORDENADO)
1 74.84 61.632 78.85 66.53
3 72.36 68.53
4 73.40 68.92
5 72.10 70.17
6 73.42 71.06
7 80.89 71.59
8 78.78 72.10
9 71.06 72.36
10 71.59 73.40
11 68.92 73.42
12 68.53 74.84
13 77.29 77.29
14 70.17 78.78
15 84.65 78.85
16 61.63 80.89
17 83.13 83.13
18 66.53 84.65
19 89.50 86.30
20 95.79 89.50
21 86.30 95.79
PROMEDIO 76.18
DESV.EST 8.2762188196
PRUEBA DE CHI CUADRADO
NC = 1 1.33!N (N)
NC = 5
"# = (#MA#$#MIN)%(NC$1)
"# = 9
CA!CU!O DE &RCUENCIA ACUMU!ADA'
INTERVALOS DE CLASE Xi.fi
1 2 3 4
MARCAS DECLASE
FRECUENCIAABSOLUTA
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61.63 0.00 0.00
61.63 70.63 66.13 5.00 330.63
70.63 79.63 75.13 10.00 751.25
79.63 88.63 84.13 4.00 336.50
88.63 97.63 93.13 2.00 186.25
97.63 106.63 102.13 0.00 0.00
21.00 1604.63
X 76.41
S 8.19
CA!CU!O DE !A &RECUENCIA ABSO!UTA
INTERVALOS DE CLASE LIMITE DE CLASE
1 2 3 4
61.63 $1.80 0.42507
61.63 70.63 66.13 $1.26 0.32894
70.63 79.63 75.13 $0.16 0.01197
79.63 88.63 84.13 0.94 0.34134
88.63 97.63 93.13 2.04 0.47558
97.63 106.63 102.13 3.14 0.49841
4.71
*+,- + / *+ = $1$ 2
N / + - * *
D /* * /* A.8 + / *: + - '
# ;2 = 5.99
# ;2 < # ;2
AREA BAJO LACURVA NORMAL
C*/
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(Xi-X !2.fi
" # $
FRECUENCIARELATIVA
FRECUENCIAACUMULADA
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0.00
528.98 0.238095 0.238095
16.53 0.476190 0.714286
238.04 0.190476 0.904762
558.73 0.095238 1.000000
0.00 0.000000 1.000000
1342.29 1.00
ei i
" # $
0.0961 8.00 5.00
0.3409 27.00 10.00
0.3294 26.00 4.00
0.1342 11.00 2.00
0.0228 2.00 0.00
# ;2 39.81
FRECUENCIARELATIVA
FRECUENCIAACUMULADA
FRECUENCIAACUMULADA
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PRUEBA DE SMIRNOV KOLMOGOR
m Q Q = X
1 61.476 5 .!1 . 4761" #1.1$ 7!.%5 5 5%.61 . "5$!%1 # .5%! %1.46"5 61.4% .14$%571 # .$54 5%.61 5 6".!1 .1" 476$ #1.$$5 6".! 5 7 .74 .$!% "5$ # .776 77.657 7!.64 .$%5714! # .417 7!.6!75 7!.%5 .!!!!!!! # .5%% 5 .!1 5 77.66 .!% "5$4 #1.5%" % . !75 7".5% .4$%5714 # .!1
1 7 .7!5 % . 4 .4761" 5 # .7111 7".5%$5 %1.47 .5$!% "5 # .!!1$ %".447 %4.%$ .5714$%6 . "1! %4.%1" %".45 .61" 476 # .1114 "7.$5$ "7.$5 .6666667 .4$15 1 ".%$7 "7.7 .714$%57 ."616 1!4.$ 5 1 !.!5 .761" 4% $.17 1!!.6!! 1 ".%! .% "5$!% 1."71% 1 !.!5!5 11".% .%5714$" .6%1" 11".% 5 1!!.6! ." 4761" 1.!%$ "7.6"" 1!4.$1 ."5$!%1 .44
PROMEDIO %7.!!5!75DESV.ES& $!.45147 7
'm()= ABS*+*,-#P*X-- .5$64%1"
= . 5 ' = 1.!6/*N-0 .5 .! 41 5$4
C 23 2 2 2 89 ' = .5$64%1" : ' = .! 41 5$4
P*X- m/*N;1-
C( ' = 'm()
V( 232 ' 3( 2 32 Sm2 8 >#K m ? > '@ ( (
S
X x Z
=
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V
+*,-
. 6! 1 . 15!"1 0.1147 0.2172
. %$$6 . 1$"7%1 0.1884 0.3382
. "51 . 477571 0.2172 0.3867
.111$! . 7"$46$ 0.2969 0.1884
.15!%6 . %4$!5$ 0.3105 0.2969
.15!%6 .1!1%54! 0.3364 0.3664
.17!61 .15"7$!! 0.3382 0.3364
.1761" .$ 476$4 0.3664 0.1147
.$ 611 .$$$4614 0.3777 0.3801
.$177 .$5%4" 5 0.3801 0.3105
.$$!6! .! 17"5 0.3867 0.3777.$4%$5 .!$!17%6 0.3967 0.3973
.$546! .!644176 0.3973 0.3967
.$% "6 .!%57 67 0.3648 0.3648
.! 15! .41$7557 0.3618 0.2519
.!$$76 .4!"144% 0.3159 0.0541
.!556" .45!%!!% 0.2519 0.0568
.!5"4$ .4"77$$" 0.1530 0.3159
.!7%$% .5$64%1" 0.0568 0.1530
.46 17 .4"$$11 0.0541 0.3618
'= ABS +*,-#P*X-
( 2 >( N 82> 2?82 2 ( 2 8
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DIS&RIBUCI N NORMAL
DA&OSA OS P*mm-
1 1""! 74.842$ 1""4 78.850! 1""5 72.3584 1""6 73.4005 1""7 72.1006 1""% 73.4177 1""" 80.892
% $ 78.783
" $ 1 71.0581 $ $ 71.59211 $ ! 68.9171$ $ 4 68.5331! $ 5 77.29214 $ 6 70.16715 $ 7 84.65016 $ % 61.62517 $ " 83.125
1% $ 1 66.5251" $ 11 89.500$ $ 1$ 95.792$1 $ 1! 86.300
% P (mm P!2(mm f(& '
1 61.6$5 !7"7.64 6! . $"557!% #1.75%$ 66.5$5 44$5.5756! . 7 $5111 #1.166! 6%.5!! 46"6.%177% . " 5$57" # ."$44 6%."17 474".5 6"4 . "4!% "6 # .%775 7 .167 4"$!.!6111 .1 65! $% # .7$66 71. 5% 5 4".$%674 .1145!!4! # .61%7 71.5"$ 51$5.!6674 .11%"4!$ # .554% 7$.1 51"%.41 .1$$%$%5$ # .4"!" 7$.!5% 5$!5.7$%4 .1$4671 ! # .461
1 7!.4 5!%7.56 .1!1 %! $ # .!!611 7!.417 5!" . 6"4 .1!1171!6 # .!!41$ 74.%4$ 56 1.$75 7 .1!6%% 4$ # .161
ES&ACI N HUANCAPI
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1! 77.$"$ 5"74. 174 .1!74$161 .1!514 7%.7%! 6$ 6.%1!61 .1!1"64"4 .!1515 7%.%5 6$17.!$$5 .1!16$6!! .!$!16 % .%"$ 654!.46174 .117" !1" .5717 %!.1$5 6" ".7656! . "74%%1 .%41% %4.65 7165.6$$5 . %$11 $1 1. $41" %6.! 7447.6" . 656!!$1 1.$$!$ %".5 % 1 .$5 . !7"55 " 1.61$1 "5.7"$ "176. 4!4 . %!616" $.!7
&O&AL 15"".717 1$!$!1.5 7
MEDIA ARI&ME&ICA DESVIACIONX= 76.177 S=
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f(' F(' ' )
. %5 !1"$ .6! "4$7 ."%6!$1 " 5. 4447"$7 . 1!77!!!
.$ $1 1!! .7$ 47661 ."5767"15 5. 4!47 6 . 4!$4$47
.$6 4$%!6 .764"6%5 ."!%17% $ 4."764$4!! . 6!%1556.$7151"1 .774 "$7 ."!!%"4"! 4."7 $$441 . 6%!"1!4.! 647 76 .% 541%%1 ."1%7 "6" 4."4% 4!$1 . %47%51.!$"4"457 .%$"!6 1" ." 67"!4 4."! 41!%1 . "7%4 64.!4$1% 7% .%44!7$%6 .%""$6%45 4."1"1776 .1 617!6%.!5!!5%$1 .%5"1"657 .%"1%41%5 4." % %$! .11446646.!5%65%%$ .%66"!1$ .%%7"7" " 4." $166"$ .11%% 7 %.!771 511 .%""5%5$7 .%71%6%4 4.%775646$ .1!71167%.!77!5"$4 ." 1$775 .%716 4!" 4.%7715%1" .1!741"64.!"!7%!!$ ."4" 5"" .%4%47%%! 4.%411!761 .164!1 15
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.!"5!4 $$ ."57115% .%44%$$74 4.%!5!65! .16%6$%45
.!7"64$$5 ." 517 $6 .%6"15715 4.%7!!%57! .14 $!1!!
.!7%66%1$ ." $"7""" .%7 $1%5% 4.%75 $! 7 .1!" 1 %5
.!!"1%%%1 .%4 6%16% ." 111"61 4."$1"4"$6 .1 4117$%
.$% 457%4 .7%16%%66 ."! $741 4."64"6!"$ . 7$$76
.$!6$1% 7 .745"4554 ."46%$"6" 4."%%%7!6$ . 546!6 4
.1%%%16!5 .71 7% 7$ ."615456$ 5. "%$477 . !"$1!$7
.1 "1" 7" .651$4 7$ ."%1!$6"!
. $4 55$7 .55"14"75 .""6" 46" 5. 5" 5!" . !1 11
S&ANDAR%.$76$1%%$
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. $
. 4
. 6
. %
.1
.1$
.14
.16
+ 8 2 8 8 2 ( ( 2 3 2F 2 8 8 m(
.$
.$5
.!
.!5
.4
.45
C ( 3 &23
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. 5
.1
.15
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DISTRIBUCIN LOG
A O P (>>) P (ORDENADO)
1 1994 74.842 95.8
2 1995 78.850 89.5
3 1996 72.358 86.3
4 1997 73.400 84.7
5 1998 72.100 83.1
6 1999 73.417 80.9
7 2000 80.892 78.9
8 2001 78.783 78.8
9 2002 71.058 77.3
10 2003 71.592 74.8
11 2004 68.917 73.4
12 2005 68.533 73.4
13 2006 77.292 72.4
14 2007 70.167 72.1
15 2008 84.650 71.6
16 2009 61.625 71.117 2010 83.125 70.2
18 2011 66.525 68.9
19 2012 89.500 68.5
20 2013 95.792 66.5
21 2014 86.300 61.6
MEDIA 76.177
DESV.ESTANDAR 8.276
ES&ACI N HUANCAPI
_
_
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ORMAL
?=/ # @ ( )
4.5622 2.2021 . !54.4942 1.5643 . 1$!4.4578 1.2226 . $ 64.4385 1.0413 . $574.4203 0.8707 . ! %4.3931 0.6150 . !%!4.3675 0.3751 . 44!4.3667 0.3671 . 4444.3476 0.1877 . 4764.3154 $0.1147 . 4"74.2962 $0.2951 . 4%%4.2959 $0.2973 . 4%%4.2816 $0.4314 . 47$4.2781 $0.4650 . 4664.2710 $0.5314 . 454
4.2635 $0.6016 . 444.2509 $0.7202 . 41$4.2329 $0.8889 . !664.2273 $0.9412 . !514.1976 $1.2204 . $674.1211 $1.9386 . "!
4.328
0.107
.
. 1
. $
. !
. 4
. 5
. 6
dx x
e x
x f x F y
y x
y
x
==
2
00
.ln
21
21
)()(
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M &ODO D
(>3%-) ORDENADO PROBABI!IDAD
1 61.476 50.31 0.048
2 73.8505 58.61 0.095
3 81.4695 61.48 0.143
4 58.6105 69.31 0.190
5 69.305 70.74 0.238
6 77.657 73.64 0.286
7 73.6375 73.85 0.333
8 50.3105 77.66 0.381
9 80.0375 79.58 0.429
10 70.735 80.04 0.476
11 79.5825 81.47 0.524
12 89.447 84.82 0.571
13 84.819 89.45 0.619
14 97.252 97.25 0.667
15 109.827 97.70 0.714
16 134.205 103.35 0.762
17 133.633 109.83 0.810
18 103.3535 119.80 0.857
19 119.8005 133.63 0.905
20 97.699 134.21 0.952
1 CA!CU!O DE !OS PARAMETROS ESTADISTICOS
MEDIA 4.44
DESVIACION 0.264
2 ESTIMACION DE PARAMETROS METODO DE MOMENTOS
0.2060747466
F 4.317499946
3INCO NITAS
CAUDA! 70 >3%-
PERIODO 50 *G,-
PROBABI!IDAD 5
T
CAUDA! 168.29
PERIODO 0.2471562355 0.3
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PROBABI!IDAD DE NO E#EDENCIA 24.72 98.04
PROBABI!IDAD DE E#EDENCIA 75.28 1.96
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LOG GUMBEL
!O ARITMOS ( ) ORDINARIO DE!TA
3.92 $1.938 0.001 0.047
4.07 $1.197 0.037 0.059
4.12 $0.965 0.072 0.070
4.24 $0.383 0.231 0.040
4.26 $0.284 0.265 0.027
4.30 $0.089 0.335 0.049
4.30 $0.075 0.340 0.007
4.35 0.169 0.430 0.049
4.38 0.288 0.472 0.044
4.38 0.315 0.482 0.006
4.40 0.401 0.512 0.012
4.44 0.597 0.577 0.005
4.49 0.855 0.654 0.034
4.58 1.261 0.753 0.087
4.58 1.283 0.758 0.044
4.64 1.556 0.810 0.048
4.70 1.851 0.855 0.045
4.79 2.273 0.902 0.045
4.90 2.803 0.941 0.036
4.90 2.824 0.942 0.010
P
59.82
0.053
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ME&ODO GUMBE
% A*O P
1 1994 213.20
2 1995 201.20
3 1996 218.60
4 1997 195.60
5 1998 206.50
6 1999 195.50
7 2000 204.70
8 2001 204.50
9 2002 186.5010 2003 171.00
11 2004 158.10
12 2005 181.10
13 2006 198.30
14 2007 194.50
15 2008 214.50
16 2009 201.60
17 2010 208.50
18 2011 233.30
19 2012 343.10
20 2013 271.40
21 2014 201.60
: ,> + , 209.68 =+ - . E- * +* 37.96 u=
ESTIMACION DE PARAMETROS METODO DE MOMENTOS
MEDIA(#) 209.68
37.9598
VARIAN@A(S2) 1440.9496
S 37.9598
29.5972
F 209.6810
DESVIACIONTIPICA
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C ( 3 &23
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ME&ODO DE LOG PEARSON III
NUMERO DE DATOS 20
A*O 0 (m3 L%(0 ( %& - X %& !3
1994 61.476 4.119 $0.032
1995 73.8505 4.302 $0.002
1996 81.4695 4.400 0.000
1997 58.6105 4.071 $0.049
1998 69.305 4.239 $0.008
1999 77.657 4.352 $0.001
2000 73.6375 4.299 $0.003
2001 50.3105 3.918 $0.139
2002 80.0375 4.382 0.000
2003 70.735 4.259 $0.006
2004 79.5825 4.377 0.000
2005 89.447 4.494 0.000
2006 84.819 4.441 0.000
2007 97.252 4.577 0.003
2008 109.827 4.699 0.018
2009 134.205 4.899 0.0992010 133.633 4.895 0.096
2011 103.3535 4.638 0.008
2012 119.8005 4.786 0.043
2013 97.699 4.582 0.003
SUMA 88.729 0.031
#!N 4.436S/ 0.2642
CS/ 0.0989
2 ESTIMACION DE PARAMETROS METODO DE MOMENTOS
J= 409.1756K= 0.0131
#0= $0.9078
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P ARSON III
% A*O 0(M3 S (XI-X !31 1994 61.476 $17292.352199555
2 1995 73.8505 $2452.1146677977
3 1996 81.4695 $201.8358984375
4 1997 58.6105 $23701.424157362
5 1998 69.305 $5861.574350619
6 1999 77.657 $906.5825094795
7 2000 73.6375 $2570.1566618326
8 2001 50.3105 $50755.230323376
9 2002 80.0375 $388.6773751326
10 2003 70.735 $4574.6060120032
11 2004 79.5825 $466.002606262
12 2005 89.447 9.415651706913 2006 84.819 $15.9340466955
14 2007 97.252 975.1954621466
15 2008 109.827 11377.9102026548
16 2009 134.205 102961.399326261
17 2010 133.633 99237.5739922195
18 2011 103.3535 4109.9357747044
19 2012 119.8005 34217.7333872312
20 2013 97.699 1113.1022738583
SUMA 144815.77526223
DATOS (N) 18MEDIA 87.335
DES.STDR 23.451SES O 0.7430
J= 7.2450525407K= 8.713
#0= 24.212
DATO
CAUDA! 70 >3%S
PERIODO 60
PROBABI!IDAD 5
&(J) 1144.5138344691
RESU!TADOS
T
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CAUDA! 44.94
PERIODO 0.08681 1.1
PROBABI!IDAD DE NO E#EDENCIA 8.68 98.36
PROBABI!IDAD DE E#EDENCIA 91.32 1.64
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P
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44.94
0.053
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