International Journal of Mathematics and Mathematical Sciences
Volume 2009 (2009), Article ID 308518, 18 pages
doi:10.1155/2009/308518
Research Article

Properties of Matrix Variate Beta Type 3 Distribution

Arjun K. Gupta1 and Daya K. Nagar2

1Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, OH 43403-0221, USA
2Departamento de Matemáticas, Universidad de Antioquia, Calle 67, No. 53-108, Medellín, Colombia

Received 27 September 2008; Accepted 29 May 2009

Academic Editor: Kenneth Berenhaut

Copyright © 2009 Arjun K. Gupta and Daya K. Nagar. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.