Estimation Of Exponential Distribution Parameter Under Mlinex Loss Function Based On Censoring Data

With the development of statistical decision theory and Bayesian theory,the Bayesian estimation problems of distribution parameters under different loss functions have been the research direction of many scholars.Nowadays,reliability analysis of products has been paid more and more attention.However,the statistical inference of exponential distribution parameters has been studied in a large number of literatures,the estimation of parameters in truncated cases is relatively small.Since Podder C.K.and Roy M.K.argued Mlinex loss function in 2003,it has caused the attention of many scholars.Based on previous studies,this paper analyzes the estimations of exponential distribution parameter under Mlinex loss function based on Censoring,such as the Bayesian estimations,the admissibility of the estimation and the empirical Bayesian estimation.First,using the parameter estimation method,I obtain the MRE estimation,the general form of the Bayesian estimation and Bayesian estimation when the prior distribution is determined under the Mlinex loss function on Type II Censoring.And I also learn about the admissibility of the relevant estimation under the Mlinex loss function.And then,the Parametric Empirical Bayes Estimation of the scale parameter is constructed under the condition that part of the hyper parameters is unknown and all the hyper parameters are completely unknown.Next,the numerical simulation is carried out by using Matlab and the results show that this estimation method is feasible.Then,the Bayesian estimation of the exponential distribution parameter under the Mlinex loss function in the case of the Type I Censoring is obtained,and it is proved that the Bayesian estimation is admissible,and then I also show its numerical simulation.Finally,I make a summary and put forward further research prospects.