This paper develops alternative brand purchase models. These models are based on distinct assumptions about the product class purchasing process over a fixed time-period. In each case, the brand choice process conditioned on a product purchase being made is assumed to be heterogeneous zero order. New analytical closed-form results are derived. These results include various market statistics such as the brand penetration, the mean and variance of the brand purchase distribution and the aggregate brand purchase distribution itself. These theoretical expressions are based on the assumption of independence between brand choice probability and mean product purchase rate across the population.
BEMMAOR, A.C. (1981). Stochastic Modeling of Consumer Purchase Behavior: I. Analytical Results. DR-81006, ESSEC Business School Research Center.