A Probablistic Market Model of Purchase Timing and Brand Selection

A stochastic model of consumer purchase behavior for frequently purchased, low cost products is developed. Both brand selection and purchase timing are incorporated in the model; a first-order Markov process is used to describe brand selection, and Erlang density functions are used to describe time between purchases. The market's behavior is obtained by describing the individual consumer's behavior and then aggregating over consumers. The model's predictions of various aggregate purchase timing statistics and repeat purchase sequences are empirically verified.