Doubly singular matrix variate beta type I and II and singular inverted matricvariate $t$ distributions

TL;DR

This paper derives the densities of doubly singular matrix variate beta type I and II distributions, their eigenvalues, and introduces the density of a singular inverted matricvariate t distribution.

Contribution

It provides new explicit density functions for doubly singular matrix variate beta distributions and the singular inverted matricvariate t distribution.

Findings

Derived densities of doubly singular beta type I and II distributions.

Obtained joint densities of their nonzero eigenvalues.

Established the density of a singular inverted matricvariate t distribution.

Abstract

In this paper, the densities of the doubly singular beta type I and II distributions are found, and the joint densities of their corresponding nonzero eigenvalues are provided. As a consequence, the density function of a singular inverted matricvariate t distribution is obtained.