Extension of the Olkin and Rubin Characterization to the Wishart distribution on homogeneous cones

TL;DR

This paper extends the Olkin and Rubin characterization of the Wishart distribution from symmetric matrices to the more general setting of homogeneous cones, broadening the theoretical understanding of these distributions.

Contribution

It generalizes the Olkin and Rubin characterization to Wishart distributions on homogeneous cones, expanding the theoretical framework beyond symmetric matrices.

Findings

Extended the Olkin and Rubin characterization to homogeneous cones.

Provided a new theoretical foundation for Wishart distributions on these cones.

Broadened the applicability of Wishart distribution characterizations.

Abstract

The Wishart distribution on an homogeneous cone is a generalization of the Riesz distribution on a symmetric cone which corresponds to a given graph. The paper extends to this distribution, the famous Olkin and Rubin characterization of the ordinary Wishart distribution on symmetric matrices.