Bimatrix Variate Beta Type IV Distribution: Relation to Wilks's Statistic and Bimatrix Variate Kummer-Beta Type IV Distribution

Abstract

In this article, 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.

Keywords:

• Bimatrix variate beta type IV distribution
• Bimatrix variate Kummer-beta type IV distribution
• Hypergeometric function of matrix argument
• Invariant polynomials
• Meijer's G-function
• Moment generating function
• Wilks's statistic
• Wishart distribution

Mathematics Subject Classification:

• Primary 62H10
• Secondary 62E15

Acknowledgment

The authors thank anonymous referees for several comments that helped to improve this article. This work is based upon research supported by the National Research Foundation, South Africa (FA2007043000003) and the Research and Development Programme (University of Pretoria).