Types Of Distribution Parameter Estimation, Bayes Inference Of Loss And Risk Functions

Bayes analysis is a kind method that introduces the information ofprior experiment to deal with the problem of decision. Bayes analysis hadbecome a complete theory system. Loss function and risk function aretwo important conceptions in Bayes conclusion. And the Bayesconclusions of the loss function and risk function of parameter estimationare now quick developing with the development of the Bayes theory andcalculation.At home and aboard, Bayes estimation of unknown parameter forseveral distributions have discussed by many scholars. And the propertiesof the Bayes estimation are discussed. Such as: Li Yang discussed theBayes conclusion of the loss function of normal distribution mean. LiuHuanxiang discussed the Bayes conclusion of the loss function and riskfunction of the dimension parameter in a special kind of dimensiondistribution family. This paper discussed the Bayes conclusion of the lossfunction and risk function of unknown parameter in binominaldistribution. And under the conjugate prior distribution, this paperinvestigates the Bayes estimations and the conservative property of theloss and risk function for the estimators of parameter of uniformdistribution. We also discuss the rationality of the Bayes estimations.For a kind of distribution as follows: F(t)=[g(t)]^θ,A≤t≤B,θ＞0In this case g(t)is gradual increase differentiable function for t,and g(A)=0,g(B)=1. The document [35] discussed the Bayesconclusion of the loss function and risk function of the unknownparameterη=1/θin conjunction prior distribution. The document[36]discussed the empirical Bayes and likelihood inference of theunknown parameter. This paper discussed that the unknown parameterηhas super bound, and its super boundη₀ has prior distribution. Inthis case, this paper discussed the Bayes conclusion and the keepingnature of the loss function and risk function.