A generalization of the bivariate Beta-Binomial distribution

This paper presents a new bivariate discrete distribution that generalizes the bivariate Beta-Binomial distribution. It is generated by Appell hypergeometric function F₁ and can be obtained as a Binomial mixture with an Exton's Generalized Beta distribution. The model has different marginal distributions which are, together with the conditional distributions, more flexible than the Beta-Binomial distribution. It has non-linear regression curves and is useful for random variables with positive correlation. These features make the model very adequate to fit observed data as the two applications included show.