Parameter Estimation Of Rayleigh Distribution With Missing Data

Rayleigh distribution is an important continuous life distribution in probability theory and statistics.It is a special type of Weibull distribution,that is,the parameter is.In recent years,statistical inference of incomplete missing data on life distribution has attracted much attention.EM algorithm is an iterative method.MLE is a very effective parameter estimation method,but when there are redundant parameters or data truncated or missing in the distribution,it is very difficult to obtain the MLE.So Dempster et al.proposed EM algorithm,which is mainly used to calculate the posterior distribution mode,and it is very suitable for processing incomplete missing data.Each iteration of the algorithm consists of two steps: the first step is to seek expectations(step E),so that the redundant parts can be removed and the missing parts can be added,and the second step is to maximize(step M).This paper is divided into five chapters.Chapter 1 briefly expounds the background,significance and progress of the research on missing data.Chapter 2summarizes the theoretical basis of relevant missing data.In the third chapter,we first introduce the left truncated right censored data model,and give the corresponding methods to complete the data,so that the missing data model can be transformed into complete data,and then we use maximum likelihood method and EM algorithm to estimate the parameters of Rayleigh distribution.When using EM algorithm,the expression of expectation in E step can be calculated directly using EM algorithm.The results of random simulation by R software show that the estimation obtained by EM algorithm is more stable and accurate than maximum likelihood estimation.Chapter 4 gives the model of Random Censoring Test Model with Incomplate Information,which is called IIRCT data.Correspondingly,the method of completing the data is proposed,which makes the missing model be transformed into a likelihood function under complete data.The parameters of Rayleigh distribution are estimated by maximum likelihood estimation,EM algorithm and Bayes estimation,respectively.When using EM algorithm,it is impossible to calculate the expected expression of data in step E,which is very difficult.So the alternative research method is Monte Carlo EM algorithm estimation.At the same time,random simulation experiments are carried out by R software.The results show that there is no difference between MCEM estimation and Bayes estimation,and they are close to the real parameters.In Chapter 5,on the premise that the prior distribution is exponential in the case of lefttruncated and right censored data,Bayes estimators of Rayleigh distribution parameters are studied under the loss functions of entropy loss and symmetry loss,Linex loss and quadratic loss,square loss and equilibrium loss,respectively,and their estimates are proved to be admissible.Then Monte Carlo method is used to carry out simulation experiments.When the Linex loss function and the balance loss function are relatively small,the Bayes estimation of parameters is better,and the approximation degree with the true value is higher,and it tends to be robust.