加权p、q对称损失函数下Burr分布参数的Bayes估计  

Bayes Estimations of Burr Distribution under the Weighted p,q Symmetric Loss Function

作　　者：于雪松 徐宝[1] YU Xuesong;XU Bao(College of Mathematics and Computer Science,Jilin Normal University,Siping Jilin 136000,China)

机构地区：[1]吉林师范大学数学与计算机学院,吉林四平136000

出　　处：《广西师范大学学报（自然科学版）》2024年第6期186-193,共8页Journal of Guangxi Normal University:Natural Science Edition

基　　金：国家自然科学基金(11571138);吉林省科技发展计划项目(YDZJ202201ZYTS622)。

摘　　要：在加权p、q对称损失函数下,利用Bayes参数估计方法研究Burr分布参数Bayes估计的形式和估计的性质,得到参数Bayes估计的一般形式以及在无信息先验分布和共轭先验分布下的精确形式,并证明所得估计具有可容许性和最小最大性,进一步得到参数的多层Bayes估计。最后用R软件结合MCMC算法对所得估计进行数值模拟,结果表明在共轭先验分布下的Bayes估计比无信息先验分布下的Bayes估计精度更高。The forms and properties of Bayes estimates of the Burr distribution parameters are investigated using the Bayes parameter estimation method under the weighted p,q symmetric loss function.The general form of the Bayes estimation of the parameters and the exact form under the uninformative prior distribution are obtained,and the obtained estimates are proved to be admissible and have the property of minimum maximum,and the multilayer Bayes estimation of the parameters is further obtained.Numerial Simulation with R software combined with MCMC algorithm on the obtained estimates shows that the Bayes estimate under the conjugate prior distribution is more accurate than the Bayes estimate under the uninformative prior distribution.

关 键 词：BURR分布 损失函数 BAYES估计 可容许性 MCMC算法 

分 类 号：O212.8[理学—概率论与数理统计]