The authors present a general framework for purchase frequency modeling that enables flexible fitting and convenient computation. Their easily described purchase frequency distributions subsume many previous models and provide a connection between mixed Poisson marketing models and the conceptually distinct compound Poisson models. These distributions provide simple parametric equations for individual-level prediction of second-period purchase frequency based on observed first-period purchase frequencies. The results are applied to four marketing panel data sets.
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References
1.
BenishayHaskel (1965), “A Disaggregate Model for the Generation of Sales,”Journal of Marketing Research, 2(February), 74–79.
2.
BenishayHaskel (1967), “Random Sums of Random Variables as Economic Processes: Sales,”Journal of Marketing Research, 4(August), 296–302.
3.
ChatfieldC., and GoodhardtG. J. (1973), “A Consumer Purchasing Model With Erlang Inter-Purchase Times,”Journal of American Statistical Association, 68(344), 828–35.
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.
EhrenbergA. S. C. (1959), “The Pattern of Consumer Purchases,”Applied Statistics, 8(1), 26–41.
6.
EhrenbergA. S. C. (1988), Repeat-Buying: Facts, Theory and Applications.London: Griffin Press.
7.
FellerW. (1970), An Introduction to Probability Theory and Its Application, 2d ed., Vol. 1. New York: John Wiley & Sons.
8.
JohnsonN. L., and KotzS. (1969), Distributions in Statistics: Discrete Distributions.New York: John Wiley & Sons.
9.
KahnB. E. (1987), “A Theoretical Model of Interpurchase Times,”Applied Stochastic Models and Data Analysis, 3(2), 93–109.
10.
KotzS., and JohnsonN. L., eds. (1982), Encyclopedia of Statistical Sciences, Vols. 1–9. New York: John Wiley & Sons.
11.
LawrenceRaymond J. (1980), “The Lognormal Distribution of Buying Frequency Rates,”Journal of Marketing Research, 17(May), 212–20.
12.
MassyWilliam R, MontgomeryDavid B., and MorrisonDonald G. (1970), Stochastic Models of Buying Behavior.Cambridge, MA: The MIT Press.
13.
MorrisonD. G., and SchmittleinD. C. (1981), “Predicting Future Random Events Based On Past Performance,”Management Science, 27(9), 1006–23.
14.
MorrisonD. G., and SchmittleinD. C. (1988), “Generalizing the NBD Model for Consumer Purchases: What Are the Implications and Is It Worth the Effort?”Journal of Business and Economic Statistics, 6(2), 145–59.
15.
MontgomeryDavid B. (1988), “On the Negative Binomial Distribution: Comment on Morrison and Schmittlein,”Journal of Business and Economic Statistics, 6(2), 163–64.
16.
PanjerH. H. (1986), “Direct Calculation of Ruin Probabilities,”Journal of Risk and Insurance, 53(3), 521–29.
17.
PanjerH. H., and WillmotG. E. (1983), “Compound Poisson Models in Actuarial Risk Theory,”Journal of Econometrics, 23(1), 63–76.
18.
PanjerH. H., and WillmotG. E. (1992), Insurance Risk Models.Schaumburg, IL: The Society of Actuaries.
19.
RobbinsH. (1977), “Prediction and Estimation for the Compound Poisson Distribution,” in Proceedings of the National Academy Science USA, Vol. 74, Washington, DC: National Academy of Sciences of the USA, 2670–71.
20.
SchmittleinD. C., BemmaorA. C., and MorrisonD. G. (1985), “Why Does the NBD Model Work? Robustness in Representing Product Purchases, Brand Purchases and Imperfectly Recorded Purchases,”Marketing Science, 4(3), 255–66.
21.
SchmittleinD. C., and MorrisonD. G. (1983), “Prediction of Future Random Events With the Condensed Negative Binomial Distribution,”Journal of American Statistical Association, 78, 449–55.
22.
SichelH. S. (1982), “Repeat-buying and the Generalized Inverse Gaussian-Poisson Distribution,”Applied Statistics, 31(3), 193–204.
23.
ThyrionP. (1969), “Extension of the Collective Risk Theory,”Skandinavisk Aktuarietidskrift, 52(Supplement), 84–98.
24.
TuckerH. G. (1967), A Graduate Course in Probability.New York: Academic Press.
25.
Van HarnK. (1978), Classifying Infinitely Divisible Distributions by Functional Equations, Mathematics Centre Tracts 103. Amsterdam: Mathematics Centre.
26.
WillmotG. E., and PanjerH. H. (1987), “Difference Equation Approaches in Evaluation of Compound Distributions,”Insurance: Mathematics and Economics, 6(1), 43–56.
27.
ZufrydenF. S. (1977), “A Composite Heterogeneous Model of Brand Choice and Purchase Timing Behavior,”Management Science, 24(7), 121–36.