Estimation For Zero-failureprobability Of Poisson Distribution Under Q-Symmetric Entropy Loss Function

Bayes statistics is one of the most important branches in Mathematical Statis-tics.During the argument with classical statistics, The Bayes statistics has been growing.As to statistical model, the basic problem is parameter estimation followed by furtherstatistical analysis which depends on the estimation results. Though there exist variouskinds of parameter estimators in literatures, it has always been an important researchsubject to measure the performance of these different estimators from the view of statis-tic decision, and the admissibility of parameter estimation is just one of the importantstatistical tools to solve such problem.The question of admissibility may depend quite sensitively on features of the lossfunction. The paper deals with the Bayes estimation for the zero-failureprobability ofpoisson distribution is e^-λ under Q-symmetric entropy loss, then discuss the admissi-bility and inadmissibility of estimator with the form of c^(T+α)/2q,and propose the Bayesestimator for the two-sample population parameters of poisson distribution under or-dered restriction.The structure of this paper is as follows:Chapter 1 is the introduction. It introduces the development of the Bayes theoryincluding the relative theory and main work of my paper.Chapter 2 is the key part of my paper, it includes 3 parts. The first part showthe Bayes estimation of zero-failureprobability of poisson distribution,the second partdiscuss the admissibility and inadmissibility of estimator with the form of c^(T+α)/2q the lastpart show the numerical experiment and the resultChapter 3 given a Bayes estimator for the two-sample population parameters ofpoisson distribution under ordered restriction. Finally the article make a summary andoutlook.