EM Algorithms And Simulation Of Parameter Estimation For Finite Mixed Distribution Model

As one of the most important methods for parameter estimation, the maximum likelihood meth-ods has been highly recommended by many scholars including statisticians due to its excellent statis-tical properties. However, real data are usually in incomplete sample situations, and the likelihood estimation of the corresponding parameter. In order to overcome this difficulty, EM algorithm was developed as an iterative algorithm to solve the parameter maximum likelihood estimation under incomplete-data situation. In this algorithm, the optimizations of complex likelihood functions are turned into optimizations of a series of relatively simple functions by data expansion.In this papers, we study the parameter estimation of the finite mixture distribution model, and perform a random simulation with R software. Firstly, this paper introduces the EM algorithm and its related theories;and then investigate the parameter estimation of the finite mixture Binomial dis-tribution model and the normal distribution model. Regarding the observed data as incomplete-data, we obtain the iterative formula of the corresponding EM algorithm, and perform a random simula-tion with R software to illustrate the effectiveness and convergence of the obtained EM algorithm. Again, this paper introduces the parameter estimation of the Multilayer model and Binomial-Poisson-Exponential distribution model is given iteration formula of the EM algorithm, using R software is simulated and compared. Finally, we study the multivariate mixed distribution model, get the sec-ond order mixed multivariate normal distribution model and the second order mixed Multinomial distribution model parameter estimation iteration formula of EM algorithm.