Extended matrix variate gamma and beta functions

Daya K. Nagar, Alejandro Roldán-Correa and Arjun K. Gupta

Journal of Multivariate Analysis, 2013, vol. 122, issue C, 53-69

Abstract: The gamma and beta functions have been generalized in several ways. The multivariate beta and multivariate gamma functions due to Ingham and Siegel have been defined as integrals having the integrand as a scalar function of the real symmetric matrix. In this article, we define extended matrix variate gamma and extended matrix variate beta functions thereby generalizing multivariate gamma and multivariate beta functions defined by Ingham and Siegel. We study a number of properties of these newly defined functions. We also give some applications of these functions to statistical distribution theory.

Keywords: Beta function; Extended beta function; Extended matrix variate beta distribution; Extended gamma function; Gamma function; Matrix argument; Transformation (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (4)

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DOI: 10.1016/j.jmva.2013.07.001

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