Determining how regularly purchases occur is an elemental step in modeling and interpreting several aspects of purchase behavior. Methods that calculate regularity at the individual level lack power when the number of observations is small and are confounded by nonstationary behavior when the number of observations is large. The authors present a summary statistic to calculate purchase regularity across consumers, using at a minimum only two interpurchase times per customer.
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References
1.
BuchananBruce S., and MorrisonDonald G. (1987), “Sampling Properties of Rate Questions With Implications for Survey Research,”Marketing Science, 6 (Summer), 286–98.
2.
ChatfieldC., and GoodhardtG. J. (1973), “A Consumer Purchasing Model With Erlang Interpurchase Times,”Journal of the American Statistical Association, 68 (December) 828–35.
3.
ConoverW. J. (1980), Practical Nonparametric Statistics, 2nd ed.New York: John Wiley & Sons, Inc.
4.
DunnR., ReaderS., and WrigleyN. (1983), “An Investigation of the Assumptions of the NBD Model as Applied to Purchasing at Individual Stores,”Applied Statistics, 32 (3), 249–59.
5.
GuptaSunil (1988), “Impact of Sales Promotions on When, What, and How Much to Buy,”Journal of Marketing Research, 25 (November), 342–55.
6.
HerniterJ. (1971), “A Probabilistic Market Model of Purchase Timing and Brand Selection,”Management Science, 18 (December), 102–13.
7.
JeulandAbel P., BassFrank M., and WrightGordon P. (1980), “A Multibrand Stochastic Model Compounding Heterogeneous Erlang Timing and Multinomial Choice Processes,”Operations Research, 28 (March-April), 255–77.
8.
JohnsonN. L. (1960), “An Approximation to the Multinomial Distribution,”Biometrika, 47, 93–102.
9.
KahnBarbara E., and MorrisonD. G. (1989), “A Note on Random Purchasing: Additional Insights From Dunn, Reader & Wrigley,”Applied Statistics, 38 (1).
10.
LawrenceRaymond J. (1980), “The Lognormal Distribution of Buying Frequency Rates,”Journal of Marketing Research, 17 (May), 212–20.
11.
MorrisonDonald G. (1973), “Some Results for Waiting Times With an Application to Survey Data,”The American Statistician, 27 (5), 226–7.
12.
MorrisonDonald G., and SchmittleinDavid C. (1988), “Generalizing the NBD Model for Consumer Purchases: What Are the Implications and Is It Worth the Effort?”Journal of Business Economics and Statistics,6 (April), 145–59.
13.
MosimannJames E. (1962), “On the Compound Multinomial Distribution, the Multivariate Beta Distribution, and Correlations Among Proportions,”Biometrika, 49, 65–82.
14.
SchmittleinDavid C., and MorrisonD. G. (1983), “Prediction of Future Random Events With the Condensed Negative Binomial Distribution,”Journal of the American Statistical Association, 78 (382), 449–56.
15.
ShapiroS. S., and WilkM. B. (1972), “An Analysis of Variance Test for the Exponential Distribution (Complete Samples),”Technometrics, 14, 355–70.
16.
WagnerUdo, and TaudesAlfred (1986), “A Multivariate Poly a Model of Brand Choice and Purchase Incidence,”Marketing Science, 5 (3), 219–44.
17.
WheatRita (1987), “Determining the Regularity of Consumers’ Interpurchase Times: Modelling, Measurement and Estimation Issues,” unpublished doctoral dissertation, Graduate School of Business, Columbia University.