The Bayesian Estimation Of Inverse Gaussion Distribution Parameter

The Empirical Bayes theory was proposed by Statistician H.Robbins in 1955. TheFamous Statistician J.Neyman considered it's"a breakthrough"in Statistical. As awidely used technology, it was concerned by people in recent decades.Inverse Gaussion distribution was proposed by Tweedie in 1945 and named bythe inverse relationship between its moment generating function and the normal distri-bution's moment generating function .Tweedie gave the basic characteristic of inverseGaussion distribution,established a number of important properties,and gave its simil-iar statistical properties with the normal distribution. Since then,the inverse Gaussiondistribution was caused by the mathematical community's attention, and has been fur-ther research and application.Inverse Gaussion distribution has many good statisticalproperties ,in many areas has broad prospects,and has been widely used in life testing,management science,actuarial science,Entomology and other fields.chapter 2 and chapter 3 discussed the Bayesian of inverse Gaussion distributionparameter under the entropy loss function and Linex loss function. In the case ofμknown,give a general form of the admissibility estimator.Then consider hierarchicalBayes estimator and E-Bayes estimator of the parameter under the prior taking intohierarchical parameters.In the case of identically independently distribution(i.i.d.)samples,empirical Bayesestimation for parameter of inverse Gaussion distribution is discussed in chapter 4,re-spectively,the Bayes rules and the empirical Bayes rules for parameter of inverse Gaus-sion distribution is constructed by using the kernel-type density estimation.The asymp-totically convergence rates for the proposed empirical Bayes estimation is obtained un-der suitable conditions.Finally ,one example about the main result s of chapter 4 are given,respectively.