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In this paper, we propose a matrix-variate generalization of the Gauss hypergeometric distribution and study several of its properties. We also derive probability density functions of the product of two independent random matrices when one of them is Gauss hypergeometric. These densities are expressed in terms of Appell’s first hypergeometric function F1 and Humbert’s confluent hypergeometric function Φ1of matrix arguments. [ABSTRACT FROM AUTHOR]

Abstract: In this article, we derive several properties such as marginal distribution, moments involving zonal polynomials, and asymptotic expansion of the complex bimatrix variate beta type 1 distribution introduced by Dı´az-Garcı´a and Gutiérrez Jáimez [José A. Dı´az-Garcı´a, Ramón Gutiérrez Jáimez, Complex bimatrix variate generalised beta distributions, Linear Algebra Appl. 432 (2010) 571–582]. We also derive distributions of several matrix valued functions of random matrices jointly distributed as complex bimatrix variate beta type 1. [Copyright &y& Elsevier]