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Bivariate count data arise in several different disciplines (epidemiology,marketing, sports statistics, etc., to name but a few) and the bivariatePoisson distribution which is a generalization of the Poisson distributionplays an important role in modeling such data. In this article, we consider theinferential aspect of a bivariate Poisson conditionals distribution for whichboth the conditionals are Poisson but the marginals are typically non-Poisson.It has Poisson marginals only in the case of independence. It appears that asimple iterative procedure under the maximum likelihood method performs quitewell as compared with other numerical subroutines, as one would expect in sucha case where the MLEs are not available in closed form. In the Bayesianparadigm, both conjugate priors and non-conjugate priors have been utilized anda comparison study has been made via a simulation study. For illustrativepurposes, a real-life data set is re-analyzed to exhibit the utility of theproposed two methods of estimation, one under the frequentist approach and theother under the Bayesian paradigm.

On classical and Bayesian inference for bivariate Poisson conditionals distributions: Theory, methods and applications