A Multibrand Stochastic Model Compounding Heterogeneous Erlang Timing and Multinomial Choice Processes

The model developed in this paper incorporates two submodels a purchase timing model which describes the occurrence over time of purchases of the product class and a multibrand stochastic choice model which specifies how any brand may be chosen on a given purchase occasion. The mathematical derivations obtained by combining both submodels lead to the identification of the formal connection between the aggregates of the market—in particular, market share, penetration, duplication and brand switching. The combining is done under the assumption of independence between the zero-order choice process and the Erlang purchase timing process. The model is fully determined when the following four types of parameters are known the market shares, m n , a measure of heterogeneity of the population in terms of choice, p , the order of the Erlang timing process, r , and two parameters which describe the distribution over the population of the purchase rate of the product class—a shape parameter k and a scale parameter c . An empirical test of the model is reported.