Study on the Significance of Recency in Computing Customer Value

7/29/2019 Study on the Significance of Recency in Computing Customer Value

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Scientific Journal of E-Business

July 2013, Volume 2, Issue 3, PP.49-53

Study on the Significance of Recency in

Computing Customer ValueLei Guo1,2#, Jie Li u1, Fuming Wu11. School of Management, Fudan University, Shanghai 200433, China

2. Shanghai Finance University, Shanghai 201209, China

#Email: [email protected]

Abstract

Recency, as the important element of customer value, has been empirically verified or directly used in many papers, especially in

papers of studying customers current and future purchase patterns. On the basis of the hypothesis about customer lifecycle and

purchase behavior proposed by Schmittlein et.al and with the theory of stochastic process, this paper deduced theoretically that

customer purchase behavior with lifecycle still has Markov property, which is so-called memorylessness. Overall, this paper

proves the significance of Recency in theory and verifies the conclusion by data.

Keywords: Customer Value; Recency; Poission D istri buti on; M arkov; M emorylessness

* 1, 2 1 1

1. 200433

2. 201209

(Recency)

Schmittlein

[1-4]

RFM (Recency)(Frequency)

(Monetary)[5, 6] Recency

[7]Guo et.al[8]

RecencySchmittlein et.al[1, 2]

Fader.et.al[9, 10] Schmittlein et.al[1, 2] Pareto/NBD

Borle Singh[3]

*

(B210)


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RFM

Rececny

Recency

1

1{ ( ), }X t t T 2n ...1 2

t t tn t Ti

, ,1 1

x x En

E ( )X t

1 1[ ( ) | ( ) , , ( ) ] [ ( ) | ( ) ],

1 1 1 1P X t x X t x X t x P X t x X t x x Rn n n n nn n n n

(1)

{ ( ), }X t t T

1nt 1nt nt , ,

1 2t t

n ( )X tn ( )1X tn

1 1

( ) , , ( )2 2

X t x X t xn n

[11]

2

Schmittlein et.al1987Management Scicence

Pareto/NBD[1]

( | ) ; 0f e

(2)

2( | ) 1 / , ( | ) 1/E Var (3)

[12]

( )[ | , ] ; 0,1, 2,...,

!

ntt

P X n t e nn

(4)

( | , ) , ( | , )E X n t t Var X n t t (5)

( ), 0N t t n n

Wn , , ,1 2W W Wn ( , ]a a t

n{ , 1W nn

}n[11]

1n

Wn , n (Erlang)

[13]


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{ , 1nW n }

1 1T , =Wn 1

W T Wn n

(6)

Tn -1n n T1 1W

Tn

Tn , 1T nn ( )E [13]

( | ) ( ); 1nT t E n (7)

1 ( | )T tn ( | )T tn

( | ) ; 1nt

t t e n

(8)

t

( | ) , 1nt

T T t e n

(9)

3

( | ) 10t t

P t e d e

(10)

tT t

( | ) 1 ( | ) 1 (1 )t t

P T t P t e e

(11)

( )( , )

( | ) ( )( )

u s tP T s t T s e ut

P T s t s e P T tusP T s e

(12)

ss t

t s

s

s

( )'( | , ) , 1,...,

u tut tT T t e e e i ni

(13)

' ( )T Ei ( )E 1

[13]

4 A

A


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65

SAS 9.2

1:

1 MINIMUM INFORMATION CRITERION

Lag MA 0 MA 1 MA 2 MA 3 MA 4 MA 5 MA6AR 0 13.22891 13.24035 13.29202 13.30681 13.3632 13.4090 13.46732AR 1 13.22565 13.28603 13.3163 13.34042 13.39181 13.43479 13.4975

AR 2 13.26767 13.29592 13.34808 13.40255 13.44079 13.47397 13.53508AR 3 13.29252 13.34419 13.40774 13.46289 13.50219 13.53784 13.59475

AR 4 13.35514 13.38043 13.44431 13.5067 13.56633 13.5962 13.65681AR 5 13.39906 13.41616 13.46952 13.52581 13.58652 13.64217 13.68187AR 6 13.44364 13.47799 13.51594 13.57962 13.64382 13.70419 13.7164

Error series model: AR(6)Minimum Table Value: BIC(1,0) = 13.22565

MINICMinimum Information Criterion BIC

BIC(1,0) BIC ARMA(1,0)ARMA, Auto-Regressive Moving Average

AR(1)The First Order Auto-Regressive Model

AR(1) AR(1) Xt

1t

X 1X

t

2 3, ,

t tX X

2

2 AUTOCORRELATION CHECK FORWHITENOISE

To Chi- Pr >

Lag Square DF ChiSq -----------------------Autocorrelations-----------------

6 6.56 6 0.3638 0.221 -0.056 -0.166 -0.043 -0.068 -0.09112 12.72 12 0.3900 -0.172 0.055 0.083 0.098 0.044 -0.166

2 Pr>ChiSq0.05

AR(1) AR(1)

5

Recency

REFERENCES[1] Schmittlein D C, Morrison D G, Colombo R. Counting Your Customers: Who Are They and What Will They Do Next?[J].

Management Science. 1987, 33(1): 1-24.

[2] Schmittlein D C, Peterson R A. Customer Base Analysis: An Industrial Purchase Process Application [J]. Marketing Science. 1994,13(1): 41-67.


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[3] Borle S, Singh S S, Jain D C. Customer Lifetime Value Measurement [J]. Management Science. 2008, 54(1): 100-112.[4] Kumar V, Rajan B. Profitable Customer Management: Measuring and Maximizing Customer Lifetime Value [J]. Management

Accounting Quarterly. 2009, 10(3): 1-18.

[5] Sheng L, Xu X. A Method of Telecom Consumer Market Segmentation Based on the RFM Model [J]. Journal of Harbin Instituteof Technology. 2006, 38(5)758-760.

[6] Xiao-Yu Z, Xiao-Yuan H, Fu-Quan S. An Optimization Model for Promotion Mix Strategy Based on RFM Analysis [J]. ChineseJournal of Management Science. 2005, 13(1): 60-64.

[7] Liu D, Shih Y. Integrating AHP and Data Mining for Product Recommendation Based on Customer Lifetime Value [J].Information & Management. 2005, 42(3): 387-400.

[8] Guo L, Liu J, Lu X. Exploratory Analysis on Components of Customer Value[C]. The 3rd International Conference on E-Businessand E-Government, Shanghai, 2012: 6128-6132.

[9] Fader P S, Hardie B G S, Lee K L. "Counting Your Customers" the Easy Way: An Alternative to the Pareto/NBD Model [J].Marketing Science. 2005, 24(2): 275-284.

[10] Fader P, Hardie B, Berger P. Customer-Base Analysis with Discrete-Time Transaction Data [DB/OL]. Available at SSRN 596801,2004.

[11] Ross S M. Introduction to Probability Models [M]. Tenth Edition Waltham: Academic Press, 2009.[12] Malcolm Wright, Zane Kearns. Progress in Marketing Knowledge [J]. Journal of Empirical Generalizations in Marketing Science,

1998, 3(1): 1-21

[13] Feller W. An Introduction to Probability Theory and Its Applications [M]. Hoboken: John Wiley & Sons, 2008.

11981-

2009

Email: [email protected]

21963-


2008


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Study on the Significance of Recency in Computing Customer Value