Parameter Estimation Of Finite Mixture Distribution Model Based On MM Algorithm

With the rapid development of science and technology of today and the continuous improvement of human cognitive ability,the data studied become more and more complex,and its heterogeneity gradually become prominent.It is difficult for single distribution to accurately depict the data,but the finite mixed distribution model is good at the processing of such data due to its flexibility.The MM algorithm based on AD method has the ability to separate the parameters of the objective function,and can transform the difficult high-dimensional optimization problem into several lowdimensional optimization problems.Moreover,it is completely based on the observed data,and has the characteristics of simple concept,easy implementation and numerical stability.Based on the above research status,this paper first proposes a general finite mixed distribution model.Secondly,based on MM algorithm,the parameter estimation of mixed Normal distribution model,Gamma-Weibull mixed distribution model,mixed Poisson distribution model,mixed Geometric distribution model,Gamma-Poisson mixed distribution model and Normal-Poisson mixed distribution model are studied,and the parameter iterative formulas of each mixed distribution model are derived.Then,the R software is used for numerical simulation experiments.Finally,two examples are given to illustrate the application of MM algorithm in the mixed distribution model.The experimental results show that the MM algorithm is accurate,stable and efficient in estimating the parameters of the finite mixed distribution model,Thus,a complete solution mechanism based on MM algorithm is provided for the parameter estimation of finite mixed distribution model,which is conducive to promoting the development and application of the finite mixed distribution model.