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

翻译：在几个不同的学科(流行病学、营销、体育统计等,仅举几个名称)产生了二变计数数据,而作为Poisson分布法一般化的二变式Poisson分布法在模拟此类数据方面起着重要作用。在本条中,我们考虑了双变式Poisson有条件分布法的推论方面,这两个条件都是Poisson,但边缘通常是非Poisson。它只在独立的情况下才有Poisson边际数据。看来,在最高可能性方法下的一个简单的迭代程序,与其他数字分流模式相比,其运行效果相当好,正如人们所预期的那样,在一个没有MLE以封闭形式提供的情况下,这种程序将发挥得相当的作用。在Bayesian的范例中,利用了先前的共产物和非前置法,并通过模拟研究进行了比较研究。为了说明起见,重新分析了一套真实生命数据组,以展示拟议的两种估算方法的效用,一种是经常使用的方法,另一种是巴耶斯模式下的。