On the Matrix-Variate Beta Distribution

Generalized Extended Matrix Variate Beta and Gamma Functions and Their Applications

“…Now, applying the above inequality in (25), and using the integral representation of the generalized extended gamma function given in (25), we obtain the desired result.…”

“…For some recent advances the reader is refereed to Hassairi and Regaig [12], Farah and Hassairi [4], Gupta and Nagar [11], and Zine [25]. However, generalizations of the extended gamma and extended beta functions defined by (5) and (6), respectively, to the matrix case have not been defined and studied.…”

Characterization of beta distribution on symmetric cones

“…, p). Basic properties of beta and beta-Riesz distributions on Ω + are given in [5,18] and of beta distribution on Ω + in [14]. For some recent advances in extending beta distribution the reader is referred to [12].…”

Matrix-Variate Beta Generator - Developments and Application

“…Gupta and Nagar (2006) extended the work of Nadarajah and Kotz (2006) by defining a matrix-variate hypergeometric beta distribution, and a matrix-variate Kummer-beta distribution was defined by Nagar and Gupta (2002). Ehlers (2011) proposed the matrix-variate beta type V distribution, motivated from generalized hypothesis testing in a multivariate setup (see also Bekker et al (2012), Zine (2012)). Pham-Gia et al (2020) established expressions for distributions of integral powers of matrix beta variates.…”