Central matricvariate and matrix multivariate T distributions

TL;DR

This paper explores various matrix-variate distributions across different algebraic systems, deriving joint densities and extending classical distributions to complex, quaternion, and octonion cases.

Contribution

It introduces and analyzes central, nonsingular matricvariate and matrix multivariate T and beta type II distributions across real, complex, quaternion, and octonion frameworks.

Findings

Derived joint densities of singular values for real normed division algebras.

Extended classical matrix distributions to non-real algebraic systems.

Unified treatment of distributions across different algebraic structures.

Abstract

Several distributions are studied, simultaneously in the real, complex, quaternion and octonion cases. Specifically, these are the central, nonsingular matricvariate and matrix multivariate T and beta type II distributions and the joint density of the singular values are obtained for real normed division algebras.