A Bivariate Chisquare Distribution and Some of its Properties

Abstract

A correlated bivariate chisquare distribution is derived from the bivariate Wishart distribution. A theorem is established that provides elegant expression for infinite sum of the product of several gamma functions. Then it is utilized for deriving product moments of the distribution. In particular, moments of the product and ratio of two correlated chisquare variables are derived. Some applications of these moments are outlined.