Product Moments of Bivariate Wishart Distribution

Abstract

The moments of the multivariate Wishart distribution is known up to the fourth order. But the product moments of the elements, namely, the two sample variances and the correlation coefficient of the bivariate Wishart distribution, are not available in general. In this paper some product moments of an arbitrary order are derived for the three elements of the bivariate Wishart distribution. A theorem containing eight identities of infinite series involving product of two gamma functions has been established to facilitate the derivation. The general nature of the theorem indicates its use in other contexts.