It will be recalled that the classical bivariate normal distributions have normal marginals and normal conditionals. It is natural to ask whether a similar phenomenon can be encountered involving Poisson marginals and conditionals. However, it is known, from research on conditionally specified models, that Poisson marginals will be encountered, together with both conditionals being of the Poisson form, only in the case in which the variables are independent. In order to have a flexible dependent bivariate model with some Poisson components, in the present article, we will be focusing on bivariate distributions with one marginal and the other family of conditionals being of the Poisson form. Such distributions are called Pseudo-Poisson distributions. We discuss distributional features of such models, explore inferential aspects and include an example of applications of the Pseudo-Poisson model to sets of over-dispersed data.

回想一下，经典的二元正态分布具有正态边际和正态条件。很自然地要问是否会遇到涉及泊松边际和条件的类似现象。然而，从对条件指定模型的研究中知道，只有在变量独立的情况下，才会遇到泊松边际，以及两个条件都是泊松形式。为了得到一个具有一些泊松分量的灵活的依赖双变量模型，在本文中，我们将重点关注一个边际和另一类条件条件为泊松形式的双变量分布。这种分布称为伪泊松分布。我们讨论此类模型的分布特征，