The Riesz probability distribution: Generation and EM algorithm

Abstract

The Riesz probability distribution was introduced in 2001 as an extension of the Wishart one. Although the Wishart distribution was investigated in many engineering applications, the Riesz applicability seems to be forsaken. This can be explained by the lack of studies offering statistical models and algorithms dealing with this distribution. Within this framework, we extend the Bartlett decomposition to the Riesz and inverse Riesz probability distributions. We prove that they can be generated easily using gamma and Gaussian independent variates adequately parameterized. Then we develop an Expectation-Maximization algorithm to estimate the parameters of the Riesz mixture model, along with the inverse Riesz mixture. Finally, some simulations are conducted and show a good estimation of the mixture parameters and clusters number.

Keywords:

• EM algorithm
• Inverse Riesz probability distribution
• Mixture models
• Riesz probability distribution
• Wishart probability distribution