Properties of Matrix Variate Beta Type 3 Distribution

Abstract

We study several properties of matrix variate beta type 3 distribution. We also derive probability density functions of the product of two independent random matrices when one of them is beta type 3. These densities are expressed in terms of Appell's first hypergeometric function F1 and Humbert's confluent hypergeometric function Φ1 of matrix arguments. Further, a bimatrix variate generalization of the beta type 3 distribution is also defined and studied.