A systematic investigation of the estimation of the Dirichlet model : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Marketing at Massey University
The NBD/Dirichlet is a stochastic model of purchase incidence and brand choice which parsimoniously integrates a wide range of well-established empirical regularities in fast moving consumer goods markets. More recently this work has been extended into other areas such as the prescribing of pharmaceuticals, (Stern 1994); airline aviation fuel contracts, (Uncles and Ehrenberg 1990a); and the visiting of retail store chains, (Uncles and Ehrenberg 1990b). By combining the stochastic assumptions of the model, namely Poisson purchasing of products, with mean rate distributed gamma across the population, and brand choice represented by multinomial probabilities distributed Dirichlet across consumers; a number of aspects of the aggregate behaviour of consumers can be successfully predicted successfully. This thesis examines the estimation issues in the Dirichlet model, specifically, the central Dirichlet parameter S used to represent heterogenity in brand choice.