熵损失函数下幂函数分布和瑞利分布参数的Bayes估计  

Estimation of Power Function Distribution and Rayleigh Distribution Parameters under Entropy Loss Function

作　　者：彭玉灵 王洪春 PENG Yuling;WANG Hongchun(College of Mathematics Science,Chongqing Normal University,Chongqing 401331,China)

机构地区：[1]重庆师范大学数学科学学院,重庆401331

出　　处：《重庆师范大学学报（自然科学版）》2022年第4期76-79,共4页Journal of Chongqing Normal University:Natural Science

基　　金：国家社会科学基金(No.13BTJ008);重庆师范大学研究生科研创新基金(No.YKC17002);重庆市高等教育教学改革研究项目(No.213139)。

摘　　要：【目的】研究熵损失函数下幂函数分布和瑞利分布参数的Bayes估计并对它的可容许性进行验证。【方法】以幂函数分布及瑞利分布为基础,以熵损失函数为主要的损失函数通过参数估计的方法和性质进行证明和研究。【结果】证明得到任意分布在熵损失函数下参数的Bayes估计、先验分布为伽马分布熵损失函数下两个分布参数的Bayes估计,得到参数可容许性。【结论】得到参数的Bayes估计,同时得到两个分布的参数在熵损失函数下的Bayes估计是可容许的。[Purposes]The estimation of parameters of power function distribution and Rayleigh distribution under entropy loss function is studied and its admissibility is verified.[Methods]Based on the power function distribution and Rayleigh distribution,the entropy loss function is used as the main loss function to prove and study through the method and properties of parameter estimation.[Findings]It is proved that the Bayesian estimation of the parameters of any distribution under the entropy loss function and the Bayesian estimation of the two distribution parameters under the entropy loss function of the prior distribution are obtained,get parameter admissibility.[Conclusions]It is admissible to obtain estimates of the parameters and to obtain estimates of the parameters of the two distributions under the entropy loss function.

关 键 词：幂函数分布 瑞利分布 BAYES估计 熵损失函数 可容许性 

分 类 号：O212.8[理学—概率论与数理统计]