A COMPARATIVE STUDY OF DIRICHLET AND DIRICHLET MULTINOMIAL DISTRIBUTION WITH APPLICATION TO BREWERY SALES’ DATA

Abstract

Customer buying behaviour research has been a special research activity in industry due to its economic, social and developmental relevance. The distribution found by compounding the multinomial distribution with the Dirichlet distribution has been suggested as a basis for the estimation of parameters in subdivided populations. This research work attempted to study the consistency of Dirichlet cum Multinomial distribution as an hybrid distribution using Bayesian method. Sales’ data were obtained on ten products from International Breweries Ilesha for a period of ten years. Vector Generalised Linear and Additive Model (VGAM) package, Comprehensive R Archive Network (CRAN) and Microsoft excel solver (2010) were used to fit the models. However, only four out of ten products met the Dirichlet and Dirichlet Multinomial distribution criteria. It was also found that the Bayes factor of Dirichlet and Dirichlet-Multinomial distribution were within the region (10<BF<30), which indicated that both models provide a better fit for the data. The test precision of the Dirichlet indicated that the precision parameter S (1.46129) >1, while the precision parameter of Dirichlet-Multinomial S (0.004487474) <1, which implied consistency of Dirichlet-Multinomial distribution as compared to Dirichlet. Due to the mixture of Dirichlet and Multinomial, the adequacy of the model also improved significantly, the model, constituted to over 93.2% to the model adequacy and its predictive estimate can be totally relied upon in decision making and prospective planning. Hence, the research work suggested that Dirichlet-multinomial distribution is more efficient and consistent with higher precision and more adequacies in the estimate of the model without any exaggeration of the model parameter. Then the model should be used by researchers and statistician that are in this area in taking any prospective decision among others