Parameter Estimation Of The Mixture Of Two Normal Distributions Of Missing Data

The problem of estimation of the parameters of the mixture of two or more normal distribution is a traditional problem in statistics. Prom long before we have started to research it. The occurrence of sample data for which two or more normal population are mixed is prevalent in many areas of application, such as biology, physics, medicine, and economics.The problem of Parameter Estimate is one of the most familiar problem in statistical inference. Two kinds of format included in Parameter Estimate: point estimate and interval estimate, point estimate is a method which use a statistic to estimate the parameter. There are many kinds of point estimate, in which the most important two kinds are method of moments and maximum likelihood estimation. EM algorithm is a iterative method in common use of incompletion data. It is used for calculating the posterior mode.In the application of statistics, there are many methods in analysissing the data of matrix format. Traditionally in the data matrix, Each matrix elements have the actual data. They usually represent continuous variable. For example, age or income. Some variables can not be observed between times. And the data which have been observed might be missed. At this time we must face the problem of missing data. In this paper, we use the basic idea of the EM algorithm, put up a certain degree of improvement to the traditional EM algorithm, and estimate the parameters of the mixture of two normal distribution based missing data.In this paper, the content can be summarized as follows:The first part: summarizing the the problem of estimation of the parameters of the mixture of two or more normal distribution and its applied value. Introducing the problem of missing data and the work we will do.The second part: Recalling the EM algorithm's basic theory and major steps. Introducing the promotion of method, such as ECM algorithm ECME algorithm and AECM algorithm, as well as those targeted by the issue of promotion.The third part: We used EM algorithm to estimate the parameters of the mixture of two normal distribution based completeness data, and used new EM algorithm to estimate the parameters of the mixture of two normal distribution based missing data.The fourth part: Testing the estimator though data simulation by programming of MATLAB.