Selberg-Type Generalized Quadratic Forms Gamma and Beta Integrals
Keywords:Selberg-Type Integral, Multivariate normal distribution, Hermitian matrix, beta density
Although Selberg-type single positive deï¬nite symmetric matrices gamma and beta integrals have been evaluated by several authors, see e.g., Askey and Richards , Gupta and Kabe [2, 4], Mathai , and elsewhere in the vast multivariate statistical analysis literature. However, several other types of Selberg-type integrals appear to have been neglected in the literature. Thus e.g., Selberg-type integrals associated with inverse Wishart densities, inverse multivariate beta densities, their noncentral counterparts, etc, have not been explored as yet. The present paper records Selberg-type generalized quadratic forms gamma and beta integrals. Our methodology is based on hypercomplex (HC) multivariate normal distribution theory, Kabe .
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