Predicting future purchases with the Poisson log-normal model

Giang Trinh (), Cam Rungie (), Malcolm Wright, Carl Driesener () and John Dawes ()

Marketing Letters, 2014, vol. 25, issue 2, 219-234

Abstract: 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. Copyright Springer Science+Business Media New York 2014

Keywords: Probability models; Purchase frequency counts; Conditional predictions; NBD; Poisson log-normal (search for similar items in EconPapers)
Date: 2014
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)

Downloads: (external link)
http://hdl.handle.net/10.1007/s11002-013-9254-1 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:kap:mktlet:v:25:y:2014:i:2:p:219-234

Ordering information: This journal article can be ordered from
http://www.springer. ... etailsPage=societies

DOI: 10.1007/s11002-013-9254-1

Access Statistics for this article

Marketing Letters is currently edited by Joel Steckel and Peter Golder

More articles in Marketing Letters from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().