加权平衡熵损失函数下Poisson分布参数的Bayes估计  

Bayesian Estimation of Parameter of Poisson Distribution under Weighted Balanced Entropy Loss Function

作　　者：程建华[1] 毛施云 王德辉[1] CHENG Jianhua;MAO Shiyun;WANG Dehui(College of Mathematics,Jilin University,Changchun 130012,China)

机构地区：[1]吉林大学数学学院

出　　处：《吉林大学学报（理学版）》2019年第4期839-843,共5页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:11871028;11731015;11571051);吉林省科技发展计划项目(批准号:20180101216JC);吉林省教育厅“十三五”科学技术研究项目(批准号:JJKH20180115KJ)

摘　　要：首先,基于平衡损失函数的形式,给出一个加权平衡熵损失函数,并将其应用到Poisson分布中,得到了该损失函数下参数的Bayes估计.其次,在先验分布为Gamma分布的条件下,给出估计量的显式表达式,证明估计量的相合性,并利用QQ图的方法检验估计量的渐近正态性。Firstly,based on the form of the balanced loss function,we gave a weighted balanced entropy loss function and applied it to the Poisson distribution,and the Bayesian estimation of the parameter under the loss function was obtained. Secondly,under the condition that the prior distribution was Gamma distribution,we gave the explicit expression of the estimator,proved the consistency of the estimator,and tested the asymptotic normality of the estimator by using the QQ plot method.

关 键 词：加权平衡熵损失函数 BAYES估计 随机模拟 相合性 渐近正态性 

分 类 号：O212.1[理学—概率论与数理统计]