Bayesian Estimation And Characters Of Several Distribution Parameters Under Linex Loss

In this paper,Bayesian estimation and characters of exponential-Poissondistribution,exponential distribution and lognormal distribution parameters are studiedunder asymmetry Linex loss.In the first part of this article the classical statistical method of parameterestimation and the deficiencies is briefly introduced,then the Bayes statistical methodand parameter estimation method is introduced,the advantages and disadvantages ofthe commonly used loss function of square loss function are given,Thus Linex lossfunction is introduced,and made a brief introduction. Finally,briefly introduces theempirical Bayes estimation and properties.The second part is the main part of the paper:First of all,the exponential distribution parameter of the Bayes estimation isstudied under Linex loss,multiple Bayes estimation is given and proofed under Linexloss,and proves the admissible estimation.And empirical Bayes estimation of rate ofconvergence are obtained.Secondly,the exponential-Poisson distribution parameter of the Bayes estimationunder Linex loss is studied.First gives the definition of this distribution and thedistribution parameter of the Bayes estimation under Linex loss.Then empirical Bayesestimation for distribution parameter is constructed by using kernel estimation methodunder Linex loss,the convergence rate of exponential-Poisson distribution is obtainedand proved,and admissibility are proved.Again,Bayesian estimation of lognormal distribution parameters is studied andproved under Linex loss.First,Bayes estimation of logarithmic normal distributionparameter under Linex loss is given,and its admissibility is proved.For semiconductordevice life follows lognormal distribution,the reliability evaluation of Bayessemiconductor device lognormal case is given,this is an application of this paper.Finally,a comparison of the estimate between the square loss and Linex loss ismade,the simulation studies are given for using the Monte Carlo method.