| 加权平衡熵损失函数下Poisson分布参数的Bayes估计 |
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| 引用本文： | 程建华,毛施云,王德辉.加权平衡熵损失函数下Poisson分布参数的Bayes估计[J].吉林大学学报(理学版),2002,57(4):839-843. |
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| 作者姓名： | 程建华 毛施云 王德辉 |
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| 作者单位： | 吉林大学 数学学院, 长春 130012
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| 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.
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| 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 |
| 收稿时间： | 2019-01-31 |
Bayesian Estimation of Parameter of Poisson Distributionunder Weighted Balanced Entropy Loss Function#br# |
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| CHENG Jianhua,MAO Shiyun,WANG Dehui.Bayesian Estimation of Parameter of Poisson Distributionunder Weighted Balanced Entropy Loss Function#br#[J].Journal of Jilin University: Sci Ed,2002,57(4):839-843. |
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| Authors: | CHENG Jianhua MAO Shiyun WANG Dehui |
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| Institution: | College of Mathematics, Jilin University, Changchun 130012, China
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| Abstract: | Firstly, based on the form of the balanced loss function, we gave aweighted balanced entropy loss function and applied it to the Poisson distribution, and the Bayesian estimation of the parameter under theloss function was obtained. Secondly, under the condition that the prior distribution was Gamma distribution, we gave the explicit expression of theestimator, proved the consistency of the estimator, and tested the asymptotic normality of the estimator by using the QQ plot method. |
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| Keywords: | weighted balanced entropy loss function Bayesian estimation stochastic simulation consistency asymptotic normality |
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