Making sense of common Dirichlet deviations

Abstract

This paper reviews the regularly recurring deviations between buyer behaviour patterns and predictions from the NBD-Dirichlet model. Previous studies have tended to look at one or two Dirichlet Deviations in isolation; the aim here is to learn more about their managerial significance by categorising them according to their behavioural indicators, summarising their incidence and extent and relating them to the implied breaches of assumptions of the model. We replicate prior research results in a single, extensive database of 62 FMCG categories and find that the Dirichlet Deviations take three forms; slight systematic variances in expected metrics across all brands in every fitting, suggesting some failure in stationarity; certain types of persistent deviation for individual brands or groups of brands that indicate partitioning; and those that capture dynamic performance. Analysis shows that consumer purchase propensities are never quite fixed or entirely independent, yet brand performance remains close to Dirichlet prediction. Managers who use this model need to be aware of the strategic options that the deviations imply, and we discuss these. Findings also contribute to the idea that deviations might be reduced by model adaptations although the managerial simplicity of the NBD-Dirichlet sets a major challenge to this.