Abstract:
In multivariate statistics under normality, the problems of interest are random covariance matrices
(known as Wishart matrices) and "ratios" of Wishart matrices that arise in multivariate analysis of
variance (MANOVA). The bimatrix variate beta type IV distribution (also known in the
literature as bimatrix variate generalised beta; matrix variate generalization of a bivariate beta type I)
arises from "ratios" of Wishart matrices. In this paper, we add a further independent Wishart random
variate to the "denominator" of one of the ratios; this results in deriving the exact expression for the
density function of the bimatrix variate extended beta type IV distribution. The latter leads to the
proposal of the bimatrix variate extended F distribution. Some interesting characteristics of these newly
introduced bimatrix distributions are explored. Lastly, we focus on the bivariate variate extended beta
type IV distribution (that is an extension of bivariate Jones’ beta).
