Bivariate generalization of the Gauss hypergeometric distribution

Abstract

ABSTRACT: The bivariate generalization of the Gauss hypergeometric distribution is defined by the probability density function proportional to x α1−1y α2−1 (1 − x − y) β−1 (1 + ξ1x + ξ2y) −γ , x > 0, y > 0, x + y < 1, where αi > 0, i = 1, 2, β > 0, −∞ < γ < ∞ and ξi > −1, i = 1, 2 are constants. In this article, we study several of its properties such as marginal and conditional distributions, joint moments and the coefficient of correlation. We compute the exact forms of R´enyi and Shannon entropies for this distribution. We also derive the distributions of X+Y , X/(X +Y ), V = X/Y and XY where X and Y follow a bivariate Gauss hypergeometric distribution.