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MATRIX-VARIATE GAUSS HYPERGEOMETRIC DISTRIBUTION

Part of: Multivariate analysis

Published online by Cambridge University Press:  04 March 2012

ARJUN K. GUPTA  and
DAYA K. NAGAR
ARJUN K. GUPTA
Affiliation:
Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, OH 43403-0221, USA (email: gupta@bgnet.bgsu.edu)
DAYA K. NAGAR*
Affiliation:
Instituto de Matemáticas, Universidad de Antioquia, Calle 67, No. 53–108, Medellín, Colombia (email: dayaknagar@yahoo.com)
*
✉For correspondence; e-mail: dayaknagar@yahoo.com
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Abstract

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In this paper, we propose a matrix-variate generalization of the Gauss hypergeometric distribution and study several of its properties. We also derive probability density functions of the product of two independent random matrices when one of them is Gauss hypergeometric. These densities are expressed in terms of Appell’s first hypergeometric function F1 and Humbert’s confluent hypergeometric function Φ1of matrix arguments.

Keywords

beta distributionbeta functiongamma functioninvariant polynomialmatrix-variatetransformationzonal polynomial

MSC classification

Secondary: 62H99: None of the above, but in this section
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 92 , Issue 3 , June 2012 , pp. 335 - 355
Copyright
Copyright © 2013 Australian Mathematical Publishing Association Inc.

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