A Problem Of Parameter Estimation For Mixture Distribution Models

With the develepment of society- improvement of computer's storage - people's deep recognize of problem and requestment's raising,How to find useful information - mode and knowledge in a great deal of data is a focus question.Tradtional sin-gal distribution can hardly effectively solve questions.So we use mixed distribution model as a valid tool to imitate observe datas,which can trace back to 1984.During the final years,the development was slow.Now as the rapid progress in computer and the develpment of Statistics, it has been widely applied in many fields,such as biology, medicine, economy, finance, environment society, engineening and so on.In this paper, we introduce the development and research of the mixed models and describe different models' probability functions- characteristics .The mixed poisson distribution(MPD) is widely used in medicine field;the mixed exponent dis-tribution(MED) is used in engineening field;the mixed Gaussian distribution(MGD) has the most widely applicating for its characteristics.The main work in the paper is to discuss mixed models' parameters estimation and confidence interval estimation.It has the following sections:In the first sec-tion,we introduce the development and research of the mixed models.In the second section,we use moment estimation - clustering estimation - EM algorithm to estimate parameters of MPD in different contions.we use Louis algorithm to estimate confidence interval.In the third section,we discuss parameters estimations of MED using moment estimation,Bayes estimation- EM algorithm- clustering estimation and compare each other.In the forth section,we use Bayes estimation- clustering estimation, EM algorithm to estimate parameters of MGD in different contions.we introduce how to improve EM algorithm when M is unknown.