On Classical and Bayesian Inference for Bivariate Geometric Conditionals Distributions: A Brief Study

Examples and applications of bivariate count data can be found in many real-life scenarios, including but not limited to proportional odds ratio, traffic statistics, epidemiological studies etc. Bivariate geometric distributions and several different variants of bivariate geometric-type distribution are useful in modeling such data. In this article, we consider the inferential aspect of a bivariate geometric conditionals distribution for which both the conditionals are geometric, but the marginals are not geometric (it has geometric marginals only in the case of independence). The MLEs are not available in closed form, but from a small simulation study, it is evident that a simple iterative procedure under the maximum likelihood method performs quite well as compared with several other numerical subroutines. In the Bayesian paradigm, both conjugate priors and non-informative priors have been utilized and a comparison study has been made via Monte Carlo simulation.