A measure of repeat buying behaviour which makes some simple assumptions e.g. that consumers tend to have split loyalties to each of several brands. Named after the German mathematician Peter Gustav Dirichlet (1805–59), the model was developed for use in marketing in the 1980s and is used to predicts future sales performance, to analyse the extent of brand cannibalization, possible success factors for new brands, and the impact of brand loyalty programmes. Key outputs of the model are analysis and prediction on penetration of category, frequency of buying and buying behaviour (see buyer and buying behaviour), number of brands bought, and market share. The model is numerical and does not assess the emotional reasons for brand switching. The Dirichlet Model of repeat-purchase behaviour stands out as probably the most widely validated model in consumer marketing. See also double jeopardy.