Complex bimatrix variate generalised beta distributions

Abstract

In this paper, we extend the study of bivariate generalised beta type I and II distributions to the matrix variate case.

Noncentral bimatrix variate generalised beta distributions

“…Other properties of bimatrix variate generalised beta type I and II distributions are studied in Díaz-García and Gutiérrez-Jáimez (2008).…”

“….U 2 ) ′ ∈ ℜ 2m×m , then under the matrix variate versions of the transformations (1), we are interested in finding the joint density of U 1 and U 2 , where it is easy to see that the marginal densities of U 1 and U 2 are matrix variate beta type I distributions. In the central case, the matrix variate joint densities of U 1 and U 2 and of F 1 and F 2 and some properties are studied in Díaz-García and Gutiérrez-Jáimez (2008). These distributions are termed central bimatrix variate generalised beta type I and II distributions, respectively.…”

Capturing a Change in the Covariance Structure of a Multivariate Process

“…Refs. [8,9] previously described constructions of this nature. The advantage of this approach lies in the mathematical and statistical formulation of observing a change in the covariance matrix in such a sequential process, and to present this matrix-based framework and results for further future study within SPC.…”

Multimatricvariate distribution under elliptical models

“…They have been applied in hydrology, finance and other areas, see for example Libby and Novick (1982), Chen and Novick (1984), Olkin and Liu (2003), Nadarajah (2007Nadarajah ( , 2013 and Sarabia et al (2014) and the references therein. In a general setting, the bimatrix variate type distribution have been studied by several authors, see Olkin and Rubin (1964), Díaz-García, and Gutiérrez-Jáimez (2010a,b, 2011), and Bekker et al (2011, and the references therein . In particular, Ehlers (2011) presents a complete exposition of the advances in this difficult topic.…”