多元混合正态分布参数的极大似然估计  

Maximum Likelihood Estimation of Multivariate Mixed Normal Distribution Parameters

作　　者：王珊珊 宓颖[1] WANG Shan-shan;MI Ying(College of Science,Liaoning University of Technology,Jinzhou 121001,China)

机构地区：[1]辽宁工业大学理学院,辽宁锦州121001

出　　处：《辽宁工业大学学报（自然科学版）》2024年第3期199-205,共7页Journal of Liaoning University of Technology(Natural Science Edition)

基　　金：辽宁省教育厅基础研究项目(JJL202015409)。

摘　　要：从层次结构的角度出发推导总结了Reinaldo B.Arellano-Vall所提出的广义多元混合正态分布公式中混合变量的相关统计性质,结合所推导的混合变量性质,运用EM算法和协方差矩阵参数化分解方法,解决多元混合正态分布在无序约束和简单树半序约束下参数的极大似然估计问题。借助MATLAB软件编程进行数据仿真模拟,并给出其协方差矩阵在简单树半序约束下的极大似然估计结果。From the perspective of hierarchy,this paper first deduces and summarizes the statistical properties of the mixed variables in the generalized multivariate mixed normal distribution formula proposed by Reinaldo B.Arellano-Vall.Secondly,combined with the derived properties of mixed variables,the EM algorithm and the covariance matrix parametric decomposition method are used to solve the problem of maximum likelihood estimation of the parameters of multivariate mixed normal under the constraints of disorder and simple tree half-order constraints.Finally,the data simulation is carried out with the help of MATLAB software,and the maximum likelihood estimation results of the covariance matrix under the half-order constraint of the simple tree are given.

关 键 词：多元混合正态分布 EM算法 极大似然估计 序约束 

分 类 号：O21[理学—概率论与数理统计]