Matricvariate and matrix multivariate Pearson type II distributions

TL;DR

This paper develops a unified framework for studying various matrix variate distributions, including Pearson type II and beta type I, across real, complex, quaternion, and octonion cases, expanding the theoretical understanding of these distributions.

Contribution

It introduces a unified approach to analyze matrix variate distributions across different algebraic systems, deriving new distributions and joint densities for singular values.

Findings

Derived the central, nonsingular matricvariate Pearson type II distribution for real normed division algebras.

Obtained matrix multivariate beta type I distributions in the unified framework.

Established joint density formulas for singular values across algebraic systems.

Abstract

This paper proposes a unified approach to enable the study of diverse distributions in the real, complex, quaternion and octonion cases, simultaneously. In particular, the central, nonsingular matricvariate and matrix multivariate Pearson type II distribution, beta type I distributions and the joint density of the singular values are obtained for real normed division algebras.