Models and Statistical Inference for Multivariate Count Data

Abstract

We investigate different multivariate discrete distributions. In particular, we study the multivariate sums and shares model for multivariate count data proposed by Jones and Marchand. One such model consists of Negative binomial sums and Polya shares. We address the parameter estimation problem for this model using the method of moments, maximum likelihood, and a Bayesian approach. We also propose a general Bayesian setup for the estimation of parameters of a Negative binomial distribution and a Polya distribution. Simulation studies are conducted to compare the performances of different estimators. The methods developed are implemented on real datasets. We also present an example of a proper Bayes point estimator which is inadmissible. Other intriguing features are exhibited by the Bayes estimator, one such feature is the constancy with respect to the large class of priors.