This paper tests four alternative composite models of market behavior over a set of consumer panel data for three product categories (margarine, regular coffee and instant coffee). Three of these models are based on various (Condensed) NBD models to describe product purchase distributions. The fourth composite model involves the compound Inverse Gaussian distribution as a purchase timing model. In each case, the beta binomial distribution represents brand choice. The empirical results demonstrate the robustness of the NBD model to departures from its assumptions. The fit provided by the composite model involving the well-known NBD mode 1 as a purchase incidence model is best among all alternative models. The gamma distribution seems to give a better description of heterogeneity than the natural conjugate family of distribution for the Inverse Gaussian (IG) distribution. On the other hand, the IG distribution provides an adequate fit to individual interpurchase times. However, the superiority of the fit at the individual level does not offset the lack of adequacy of the model for heterogeneity in purchasing behavior across consumers.
BEMMAOR, A.C. (1981). Stochastic Modeling of Consumer Purchase Behavior: II. Applications. DR-81007, ESSEC Business School Research Center.