Selberg-Type Generalized Quadratic Forms Gamma and Beta Integrals

Authors

  • Arjun K. Gupta Bowling Green State University, Bowling Green, Ohio, USA
  • D. G. Kabe

Keywords:

Selberg-Type Integral, Multivariate normal distribution, Hermitian matrix, beta density

Abstract

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 [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].

Author Biography

  • D. G. Kabe
    Selberg-Type Generalized Quadratic Forms Gamma and Beta Integrals

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Published

2017-07-11

Issue

Section

Mathematical Statistics

How to Cite

Selberg-Type Generalized Quadratic Forms Gamma and Beta Integrals. (2017). European Journal of Pure and Applied Mathematics, 10(4), 614-619. https://www.ejpam.com/index.php/ejpam/article/view/3075