Bayes Estimation Of The Several Different Distribution

There are Bayes school and Classical school in the Statistics, the differencesbetween Bayes analysis and classical statistics are in whether the use of a prioriinformation (experience and historical data). Empirical Bayes including theparameters of the experience bayesian and the non parameters of the experienceBayesian. Parameters bayesian is that experience of prior parameters belongs to asuper parameters are unknown distribution class, estimate of Super parameters isobtained, so the estimate of the prior distribution of the parameters is obtained. Suchprocessing way that experience bayesian can get nature good result.The working of paper is the following aspects:Firstly, Bayes estimation promotes under balance loss function to under balancethe weighted loss. Pareto distribution and inverse gaussian distribution with the priordistribution respectively for Gamma distribution draw Bayes estimation under balancethe weighted loss, and Pascal distribution with the prior distribution respectively forBate distribution draw Bayes estimation under balance the weighted loss. Proving thatthe q (θ)is selected the estimate is the allowable.Secondly, For new Bayes estimation for analysis, it can be applied in Paretodistribution,PASCAL distribution, and according to the characteristics of the twokinds of distribution are given respectively more appropriate super prior distribution,which provide the basis for E Bayes estimation and multi-layer Bayes estimation.Finally, E Bayes estimation and multi-layer Bayes estimation of Paretodistribution,PASCAL distribution are respectively obtained, which increase Fittingoptimal benign of the estimation.