基于记录值的GE分布参数的Bayes和经验Bayes估计  

Bayes and Empirical Bayes Estimation of Parameter of Generalized Exponential Distribution Based on Record Values

作　　者：王琪[1] 黄文宜[2] 

机构地区：[1]电子科技大学中山学院,广东中山528402 [2]宜春学院数学与计算机科学学院,江西宜春336000

出　　处：《重庆师范大学学报（自然科学版）》2013年第4期55-58,共4页Journal of Chongqing Normal University:Natural Science

基　　金：江西省教育厅科技基金(No.GJJ11600)

摘　　要：针对来自广义指数(GE)分布的记录值样本,研究了广义指数分布的参数的估计问题。首先给出了参数的最大似然估计;在参数的共轭先验分布为贝塔先验分布,损失函数为平方误差损失和LINEX损失函数情形下,导出了广义指数分布参数的Bayes和经验Bayes估计。最后进行了Monte Carlo数值模拟,对本文提出的几种参数估计进行比较,发现在合适的先验分布条件下Bayes和经验Bayes估计值更加接近参数真实值,因此在适当的先验分布下Bayes估计和经验Bayes估计较传统的最大似然估计好。According to the record values from the generalized exponential distribution sample,parameter estimation problem of generalized exponential distribution is studied.First,the maximum likelihood parameter estimation is given;when the conjugate prior distribution of parameters for the Berta prior distribution,and the loss function is the squared error loss and LINEX loss functions,Bayes and empirical Bayes estimators of the parameter of the generalized exponential distribution are derived.Finally,a Monte Carlo numerical simulation is given to compare these estimators presented in this paper.We found in the prior distribution of the right conditions and experience of the Bayes estimates closer to the true parameters,therefore the maximum likelihood proper prior distribution of Bayes and empirical Bayes estimators are closer than the maximum likelihood estimator when the prior distribution is proper.Then Bayes and empirical Bayes estimators are better than the maximum likelihood estimator under proper prior distribution.

关 键 词：Bayes和经验Bayes估计 平方误差损失 LINEX损失 记录值 

分 类 号：O213[理学—概率论与数理统计]