A Consumer Purchasing Model with Erlang Inter-Purchase Times

Abstract The gamma-Poisson form of the negative binomial distribution (NBD) model generally gives a good fit to many aspects of repeat-buying behavior for a wide range of frequently bought branded consumer goods. Nonetheless, empirical evidence suggests that purchasing a particular brand-size in successive equal time-periods tends to be more regular than Poisson. An alternative model is therefore examined in which inter-purchase times for a given consumer are described by an Erlang distribution rather than by the negative exponential distribution implicit in the Poisson assumption of the NBD model. But it is found that the NBD model is robust to this kind of departure. Because of its greater simplicity, the NBD model therefore seems preferable for practical use.