Predicting future purchases with the Poisson log-normal model

Trinh, Giang, Rungie, Cam, Wright, Malcolm, Driesener, Carl and Dawes, John 2014, Predicting future purchases with the Poisson log-normal model, Marketing letters, vol. 25, no. 2, pp. 219-234, doi: 10.1007/s11002-013-9254-1.

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Title Predicting future purchases with the Poisson log-normal model
Author(s) Trinh, Giang
Rungie, Cam
Wright, Malcolm
Driesener, Carl
Dawes, John
Journal name Marketing letters
Volume number 25
Issue number 2
Start page 219
End page 234
Total pages 16
Publisher Springer-Verlag
Place of publication Berlin, Germany
Publication date 2014
ISSN 1573-059X
Keyword(s) market prediction
Summary The negative binomial distribution (NBD) has been widely used in marketing for modeling purchase frequency counts, particularly in packaged goods contexts. A key managerially relevant use of this model is Conditional Trend Analysis (CTA)—a method of benchmarking future sales utilizing the NBD conditional expectation. CTA allows brand managers to identify whether the sales change in a second period is accounted for by previous non-, light, or heavy buyers of the brand. Although a useful tool, the conditional prediction of the NBD suffers from a bias: it under predicts what the period-one non-buyer class will do in period two and over predicts the sales contribution of existing buyers. In addition, the NBD's assumption of a gamma-distributed mean purchase rate lacks theoretical support—it is not possible to explain why a gamma distribution should hold. This paper therefore proposes an alternative model using a log-normal distribution in place of the gamma distribution, hence creating a Poisson log-normal (PLN) distribution. The PLN distribution has a stronger theoretical grounding than the NBD as it has a natural interpretation relying on the central limit theorem. Empirical analysis of brands in multiple categories shows that the PLN distribution gives better predictions than the NBD.
Language eng
DOI 10.1007/s11002-013-9254-1
Field of Research 149999 Economics not elsewhere classified
Socio Economic Objective 970114 Expanding Knowledge in Economics
HERDC Research category C1.1 Refereed article in a scholarly journal
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Document type: Journal Article
Collections: Faculty of Business and Law
Deakin Business School
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