On Wishart distribution

TL;DR

This paper develops a unified framework for studying the Wishart distribution across real, complex, quaternion, and octonion cases, deriving key properties like eigenvalue distributions and maximum eigenvalue behavior.

Contribution

It introduces a comprehensive approach that extends Wishart distribution analysis to all real normed division algebras, including noncentral and eigenvalue distributions.

Findings

Derived joint eigenvalue density for real normed division algebras

Obtained distribution of the maximum eigenvalue

Extended Wishart distribution to quaternion and octonion cases

Abstract

This paper proposes a unified approach that enables the Wishart distribution to be studied simultaneously in the real, complex, quaternion and octonion cases. In particular, the noncentral generalised Wishart distribution, the joint density of the eigenvalues and the distribution of the maximum eigenvalue are obtained for real normed division algebras.