E - Bayesian Estimation Of Several Continuous Distributions

Bayes methods have been developed rapidly, especially the Hierarchical Bayesian prior dis-tribution was put forward by Lindly. However, this method usually related to the calculation ofintegral. Although the MCMC(Markov Chain Monte Calo) method can solve this problem,but itis inconvenient in application. This shortcoming greatly restrict the application of Bayes method.To solve this question, a recorrectde estimation ―E-Bayesian estimation was proposed by HanMing, a chinese scholar. The E-Bayes estimation is more simple and easier.This article basis in Bayes, mainly studies estimates of several distribution parameters. Andthrough numerical simulation, prove that the E-Bayesian estimation in the article is reasonableand good nature.First, in square loss function and Q-symmetric entropy loss function, mainly studies anddiscusses the E-Bayesian estimation and Hierarchical Bayesian estimation of Burr distributionparameter by using conjugate prior distribution. It proves that the two estimations is asymptoti-cally equal when the n approaches to infinite. Also, it gives the numerical simulation about theestimation and comparison of the superiority between the two.Secondly, the article discusses the E-Bayesian estimation and Hierarchical Bayesian esti-mation of Laplace distribution and Rayleigh distribution in Q-symmetric entropy loss functionrespectively. Also, it gives the numerical simulation to illustrate the relatinship and differencebetween the two estimations.The final analysis conclusions illustrate that E-Bayesian estimation and HierarchicalBayesian estimation is asymptotically equal, but E-Bayesian estimation is more useful for ap-plication.