加权平衡损失函数下逆伽马分布的Bayes估计  

Bayesian estimation of inverse gamma distribution under weighted balanced loss function

作　　者：罗琼 周菊玲[1] LUO Qiong;ZHOU Juling(School of Mathematical Sciences,Xinjiang Normal University,830017,Urumqi,Xinjiang,PRC)

机构地区：[1]新疆师范大学数学科学学院,新疆维吾尔自治区乌鲁木齐市830017

出　　处：《曲阜师范大学学报（自然科学版）》2023年第2期19-24,共6页Journal of Qufu Normal University(Natural Science)

基　　金：国家自然科学基金(11801488);新疆师范大学教学研究与改革(SDJG2020-30);新疆师范大学科研发展专项(XJNUZX202001).

摘　　要：在逆伽马分布尺度参数的先验分布为其共轭先验分布伽马分布Γ(a,b)时,给出了其在加权平衡损失函数下的Bayes估计、E-Bayes估计和多层Bayes估计.最后通过数值模拟,说明了此3种估计具有较高的稳健性和精确性,其中多层Bayes估计的稳健性最好,E-Bayes估计的精确性最好.The Bayesian estimation,E-Bayes estimation and hierarchical Bayesian estimation under the weighted balance loss function are given when the inverse gamma’s prior distribution is its conjugate prior distribution,the Gamma distributionΓ(a,b).Finally,the numerical simulation shows that the above three estimates have high robustness and accuracy,among which the hierarchical Bayesian estimation has the best robustness and the E-bayes estimation has the best accuracy.

关 键 词：加权平衡损失函数 逆伽马分布 BAYES估计 E-BAYES估计 多层BAYES估计 

分 类 号：O212.1[理学—概率论与数理统计]