A characterization of the Riesz distribution

TL;DR

This paper characterizes the Riesz distribution by using the division algorithm based on Cholesky decomposition, extending previous work on Wishart distribution characterizations with different division algorithms.

Contribution

It introduces a new characterization of the Riesz distribution through the Cholesky-based division algorithm, expanding the understanding of distribution properties.

Findings

Characterization of the Riesz distribution using Cholesky division algorithm

Extension of Wishart distribution characterization methods

Connection between division algorithms and distribution properties

Abstract

Bobecka and Wesolowski (2002) have shown that, in the Olkin and Rubin characterization of the Wishart distribution (See Casalis and Letac (1996)), when we use the division algorithm defined by the quadratic representation and replace the property of invariance by the existence of twice differentiable densities, we still have a characterization of the Wishart distribution. In the present work, we show that, when we use the division algorithm defined by the Cholesky decomposition, we get a characterization of the Riesz distribution.