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 functionΦ1 of matrix arguments. Further, a bimatrix variate generalization...

The authors would like to hereby acknowledge the support of StatDisT group. This work is based upon research supported by National Research foundation South Africa, Reference: SRUG 190308422768 grant number 120839, IFR170227223754 109214 and SARCHI Chair UID: 71199. opinions expressed conclusions arrived at are those not necessarily be attributed NRF.

In this paper the bimatrix variate beta type IV distribution is derived from independent Wishart distributed matrix variables. We explore specific properties of this distribution which is then used to derive the exact expressions of the densities of the product and ratio of two dependent Wilks’s statistics and to define the bimatrix Kummer-beta type IV distribution.