The Riesz probability distribution: Generation and EM algorithm

作     者：Kessentini, Sameh Tounsi, Mariem Zine, Raoudha 

作者机构：Fac Sci Sfax Lab Probabil & Stat Sfax Tunisia 

出 版 物：《COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION》 (统计学通讯：模拟与计算)

年 卷 期：2020年第49卷第8期

页      面：2114-2133页

核心收录：

学科分类：0202[经济学-应用经济学] 02[经济学] 020208[经济学-统计学] 07[理学] 0714[理学-统计学（可授理学、经济学学位）] 

主　　题：EM algorithm Inverse Riesz probability distribution Mixture models Riesz probability distribution Wishart probability distribution 

摘      要：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.