Several Types Of The Hybrid Model Parameter Estimation Problem

With the rapid development of the mixed model, it has had great theoretical basis, and it is applied in various aspect of social life. For example, it is very obvious in the aspects of stock and finance. In this field, it is a primary task to forecast the future direction of the data. Moreover, fitting data is the best way to solve this question. But, because of the complexity of the data, it is unable to meet the condition needed with a single model that is not very accurate. On the contrary, mixed model can solve this problem. It has a better effect than single model on all kinds of complex data. For fitting data, it is very important to estimate parameters exactly. But because mixed distribution’s density function is more complex and has more parameters to be estimated. So it is difficult to use general estimation method.To this situation, this paper has done some researches for several different types of mixture distribution and has obtianed some conclusions. The first chapter gives reason to the concept of mixed distribution and the problem need to be solved, then makes some description for EM algorithm and Bayesian formula that will be used later. The second chapter estimates the parameters of0-1mixture distribution by maximum likelihood method and obtains iterative formula. Finally, we discuss the nature of the iteration value. The third chapter introduces the concepts and the nature of mixed binomial distribution and gets the estimation value of the two order mixed binomial distribution using moment estimation method. Then I get the iterative formula of m order mixed distribution with EM algorithm. Finally, I make computer simulation for the result. In the fourth chapter, mixed Gauss distribution is discussed. I get the equations of iteration value, process a simulation calculation and obtain the density function graphics. Lastly, I process hypothesis test to the parameters. In the fifth chapter, the linear combination of different distribution is analysised. the estimation method of mixed Geometry, Poisson and Exponential distribution are given. Then the iterative formula is obtained with the method just given above. At last, I proceed the computer simulation with specific numbers and obtains the simulation results. According to the results, I obtain the graphics of density function.