Generalizing the NBD Model for Customer Purchases: What Are the Implications and Is It Worth the Effort?

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Abstract
An often-used scenario in marketing is that of individuals purchasing in a Poisson manner with their purchasing rates distributed gamma across the population of customers. Ehrenberg (1959) introduced the marketing community to this story and the resulting negative binomial distribution (NBD), and during the past 30 years the NBD model has been shown to work quite well. But the basic gamma/Poisson assumptions lack some face validity. In many product categories, customers purchase more regularly than the exponential. There are some individuals who will never purchase. The purpose of this article is to review briefly the literature that addresses these and other issues. The tractable results presented arise when the basic gamma/Poisson assumptions are relaxed one issue at a time. Some conjectures will be made about the robustness of the NBD when multiple deviations occur together. The NBD may work, but there are still opportunities for working on variations of the NBD theme.