1. Honorary Invited Paper Selberg-Type Generalized Quadratic Forms Gamma and Beta Integrals.
- Author
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Gupta, Arjun K. and Kabe, D. G.
- Subjects
- *
SELBERG trace formula , *QUADRATIC forms , *INTEGRALS , *SYMMETRIC matrices , *MULTIVARIATE analysis - Abstract
Although Selberg-type single positive definite symmetric matrices gamma and beta integrals have been evaluated by several authors, see e.g., Askey and Richards [1], Gupta and Kabe [2, 4], Mathai [8], 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 [6]. [ABSTRACT FROM AUTHOR]
- Published
- 2017