Selberg-type squared matrices gamma and beta integrals

A. K. Gupta, D. G. Kabe

Abstract

Although Selberg-type, single positive definite symmetric matrices, gamma and beta integrals are evaluated by several authors; see e.g., Askey and Richards (1989), Gupta and Kabe (2005), Mathai (1997), and elsewhere in the vast multivariate statistical analysis literature; the Selberg-type squared matrice gamma and beta interals appear to have been neglected. So also Selberg-type of integrals of positive signature symmetric matrices, skew symmetric matrices are neglected in the literature. This paper records Selberg-type squared matrices beta and gamma integrals.

Keywords

Selberg-type integrals; squared matrices integrals; hypercomplex normal distributions; multivariate gamma and beta densities.

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