熵损失函数下Burr(α)X分布参数的贝叶斯估计  

Bayes Estimation of Parameter for Burr(α) X Distribution under Entropy Loss Function

作　　者：陈家清[1] 王玉 陈志强[1] 

机构地区：[1]武汉理工大学理学院,武汉430070

出　　处：《统计与决策》2017年第20期5-9,共5页Statistics & Decision

基　　金：国家自然科学基金面上资助项目(81671633);湖北省自然科学基金资助项目(2014CFB863)

摘　　要：文章研究了Burr(α)X分布参数的各类贝叶斯估计问题。在熵损失函数下分别获得了参数的贝叶斯估计、经验贝叶斯估计、多层贝叶斯估计和E-Bayes估计。证明了参数经验贝叶斯估计的渐近最优性,讨论了参数多层贝叶斯估计和E-Bayes估计的稳健性,通过蒙特卡洛方法对各类估计的MSE进行了数值模拟和比较分析,结果表明:经验贝叶斯估计的均方误差最小,精度较高。This paper investigates all kinds of Bayes estimations of parameter for Burr （ α） X distribution, and respectively obtains Bayes estimation, empirical Bayes estimation, hierarchical Bayes estimation and E-Bayes estimation under the entropy loss function. Furthermore the paper verifies that the empirical Bayes estimation is asymptotically optimal, and at the same time discusses the robustness of the hierarchical Bayes estimation and E-Bayes estimation. Finally the paper conducts a value simula- tion and comparison of the mean square error （MSE） of various estimations based on Monte Carlo method. The study result shows that the empirical Bayes estimation has minimum MSE and high-precision.

关 键 词：BURR X分布 Bayes估计 经验BAYES估计 多层BAYES估计 E-BAYES估计 

分 类 号：O212.1[理学—概率论与数理统计]