Full paper in PDF:
$% X. Cui, A. K. Gupta, and D. K. Nagar, Wilks’ Factorization of the complex matrix variate Dirichlet distributions, Rev. Mat. Complut. 18 (2005), no. 2, 315328.%$

Wilks’ Factorization of the Complex Matrix Variate Dirichlet Distributions

Xinping CUI, Arjun K. GUPTA,
and Daya K. NAGAR
Department of Statistics
University of California-Riverside
Riverside, CA 92521 USA
Department of Mathematics and Statistics
Bowling Green State University
Bowling Green, Ohio 43403-0221 USA
Departamento de Matemáticas
Universidad de Antioquia
Medellín, A. A. 1226 Colombia

Received: July 27, 2004
Accepted: December 17, 2004

In this paper, it has been shown that the complex matrix variate Dirichlet type I density factors into the complex matrix variate beta type I densities. Similar result has also been derived for the complex matrix variate Dirichlet type II density. Also, by using certain matrix transformations, the complex matrix variate Dirichlet distributions have been generated from the complex matrix beta distributions. Further, several results on the product of complex Wishart and complex beta matrices with a set of complex Dirichlet type I matrices have been derived.

Key words: beta distribution, complex random matrix, Dirichlet distribution, Jacobian, complex multivariate gamma function, transformation, Wishart distribution.
2000 Mathematics Subject Classification:
Primary 62H10; Secondary 62E20.