On the Matrix-Variate Beta Distribution

Abstract

The Riesz distributions on symmetric matrices are used to introduce different versions of beta distributions. Some fundamental properties of these distributions are established. We prove a property of independence between blocks of a beta-Riesz, and we show that some projections of these distributions are also beta-Riesz.

Keywords:

• Beta distribution
• Cholesky decomposition
• Riesz distribution
• Symmetric matrices
• Wishart distribution

Mathematics Subject Classification:

• 60E05
• 62E10

Acknowledgments

I sincerely thank the Editor, the Associate Editor, and a referee for their suggestions and comments that led to significant improvements in this article.