Bivariate generalized Poisson distribution and its relation with 2D–Hermite polynomials

Abstract

In this paper we consider the bivariate generalized Poisson (G-P) distribution, which is derived from the confluent hypergeometric distribution using the trivariate reduction method. We study some of its important properties such as generating functions, recurrence relations, and differential equations for its probabilities. Furthermore, we show that the certain bivariate G-P distribution is related with the 2D–Hermite type polynomials. As consequence, several formulas for the 2D–Hermite polynomials are obtained.