The Research On Papameters Estimation Of The Generalized Gamma Mixture Medel

As a mathematical statistics modeling tool of analysis a wide variety of random phenomena, FMM (Finite Mixture Model) can be defined any complex probability distribution model, which has been applied in many statistical data modeling of theoretical study and practical work. Because of simple form, convenient calculation, GMM (Gaussian Mixture Model) has become widely used in the Mixture Model. However, considering that actual data has nonlinear, non-Gaussian characteristics, and limited to fitting perform of the Gaussian distribution, GMM can not fully, accurately describe and characterize these complex data. This thesis firstly presents flexibility and good fitting capability of the GGD (Generalized Gamma Distribution) as the mixture component of the FMM to define GGMM (Generalized Gamma Mixture Model), and then investigate the effective methods of parameter estimation.It is well known that, the parameter estimation of FMM can be viewed as an incomplete data problem, whose common method is EM (Expectation Maximization) algorithm proposed by Dempster in 1997. We studied based-EM algorithm for parameter estimation of the GMM derivation and numerical simulation, with fixed number of mixture components, researched EM algorithm and SEM algorithm for parameters estimation of GGMM. In order to address the issue of parameter coupling, we give EM_Raphson algorithm for parameters estimation of coupling. After, the SEM (Stochastic Expectation Maximization) is discussed. Finally, experiments verify the validity and feasibility of EM algorithm and SEM algorithm for parameter estimation of GGMM, whose perform is also compared.In order to address the problem of convergence slow, convergence to a local optimum, sensitive to initialization, the number of mixture components for modeling the distributions is known and other shortcomings of EM algorithm, presented GAEM algorithm and MDL criterion for researching parameters estimation of GGMM. We presented adaptive number of mixture components method for parameter estimation of GGMM. The more robust initial values of EM algorithm can be achieved GA algorithm, and can convergence to a global optimum. The MDL criterion is used for selecting the number of components of the GGMM. Experiments verify the validity and feasibility of GAEM for parameters estimation of GGMM, which can be provided the theoretical foundation for practical application.