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It will be recalled that the classical bivariate normal distributions havenormal marginals and normal conditionals. It is natural to ask whether asimilar phenomenon can be encountered involving Poisson marginals andconditionals. Reference to Arnold, Castillo and Sarabia's (1999) book onconditionally specified models will confirm that Poisson marginals will beencountered, together with both conditionals being of the Poisson form, only inthe case in which the variables are independent. Instead, in the presentarticle we will be focusing on bivariate distributions with one marginal andthe other family of conditionals being of the Poisson form. Such distributionsare called Pseudo-Poisson distributions. We discuss distributional features ofsuch models, explore inferential aspects and include an example of applicationsof the Pseudo-Poisson model to sets of over-dispersed data.

Statistical Inference for distributions with one Poisson conditional