An Application Of EM Algorithm For Parameter Estimation Of The Mixture Model

As one of the most important methods for parameter estimation, maximum likelihood estimation has been highly recommended by many scholars including statisticians due to its excellent statistical properties. However, real data are usually in incomplete sample situations, and the likelihood functions are sometimes too complex, thus it is very difficult to solve the maximum likelihood estimation of the corresponding parameter. To overcome this obstacle, 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.Herein we introduce EM algorithm and its related theories firstly, and then investigate the pa-rameter estimation of the mixture Poisson distribution model and the mixture normal distribution model. Regarding the observed data as incomplete-data, we obtain the iterative formula of the cor-responding EM algorithm, and perform a random simulation with R software to illustrate the effec-tiveness and convergence of the obtained EM algorithm. After studying the parameter estimation of Binomial-Poisson hierarchy, we get the iterative formula of the corresponding EM algorithm. Finally, we investigate the parameters estimation of Multiple Poisson distribution under complete-data and incomplete-data situations as well as the EM algorithm under incomplete-data situation, and perform a comparative study of the parameters estimation results according to the examples.