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