Table of Contents
ISRN Probability and Statistics
Volume 2012, Article ID 789273, 20 pages
http://dx.doi.org/10.5402/2012/789273
Research Article

Matrix Variate Pareto Distribution of the Second Kind

1Instituto de Matemáticas, Universidad de Antioquia, Calle 67, No. 53–108, Medellín, Colombia
2Department of Statistics, University of Rajasthan, Jaipur 302004, India
3Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, OH 43403-0221, USA

Received 15 August 2012; Accepted 6 September 2012

Academic Editors: J. Jiang and C. Proppe

Copyright © 2012 Daya K. Nagar et al. 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 generalize the univariate Pareto distribution of the second kind to the matrix case and give its derivation using matrix variate gamma distribution. We study several properties such as cumulative distribution function, marginal distribution of submatrix, triangular factorization, moment generating function, and expected values of the Pareto matrix. Some of these results are expressed in terms of special functions of matrix arguments, zonal, and invariant polynomials.