| There are many works and articles based on Bayesian point estimation based on different loss functions,for example,the loss function is different according to the parameter space of the estimator.Another the Bayesian criterion is different for different distribution models.In this paper,the Bayesian estimation of the(0,1)parameter space,Beta-Negative Binomial model and Zhang’s loss function is discussed.The Bayesian estimation of the parameters to be estimated is the Bayes estimator,which is called posterior estimator;And the average risk of the posterior estimator is called Bayesian risk.We also analytically calculate the usual Bayes rule under the squared error loss,which has been proved to be smaller than that under Zhang’s loss.But the posterior expectation is larger.Finally the numerical simulations and a real data example of some claim number data exemplify our theoretical studies of two size relationships about the Bayes estimators and the posterior expectations.This paper is divide into four chapters.Chapter 1,introduction.We first introduce the Bayesian method for loss function of the optimal selection conditions,Bayesian parameter,estimation method and the conjugate distribution,at the same time introduced the statistical inference model based on Bayesian method at home and abroad research status and significance in details.Chapter 2,main method.Firstly,we discuss the global unique minimizer based on Zhang’s loss function under as our estimator,the posterior expected Zhang’s loss under the Beta-Negative Binomial Model.And the estimator of the square error loss function,and its posterior expectation.Moreover,the comprehensive risk was calculated.Chapter 3,numerical simulation and a real data example.Vast amount of numerical simulation results and a real data example of some claim number data to support the theoretical studies that mentioned by Chapter two.Chapter 4,conclusion and further work.We summarize the main conclusions,and propose some interesting problems to be done. |
