两类损失函数下泊松差分布参数的Bayes估计  

Bayes Estimation of Parameters of Poisson Difference Distribution Under Two Types of Loss Functions

作　　者：王德辉 李昕炎 WANG De-hui;LI Xin-yan(School of Mathematics and Statistics,Liaoning University,Shenyang 110036,China)

机构地区：[1]辽宁大学数学与统计学院,辽宁沈阳110036

出　　处：《辽宁大学学报(自然科学版)》2025年第1期86-96,共11页Journal of Liaoning University:Natural Sciences Edition

基　　金：国家自然科学基金(12271231)。

摘　　要：本文研究在熵损失函数以及0-1损失函数下泊松差分布参数的Bayes估计问题.首先,以Bayes推断思想为基础,分别得出在两类损失函数下参数的Bayes估计.其次,通过随机模拟验证了两类损失函数下Bayes估计的相合性与渐近正态性,并且对这两类损失函数下的Bayes估计进行了比较.结果表明,两类损失函数下的Bayes估计均具有良好的估计效果,在相同样本下,熵损失函数下的Bayes估计要优于0-1损失函数下的Bayes估计.最后,利用泊松差分布对某医院每日使用床位数目的变化量进行实证分析,通过皮尔逊卡方检验,熵损失函数下的Bayes估计得到的泊松差分布与数据的拟合度较好.This paper studies the Bayes estimation of the parameters of Poisson difference distribution under entropy loss and 0-1 loss function.Firstly,based on Bayes inference,the Bayes estimation under the two losses are derived separately.Secondly,the coincidence and asymptotic normality of the Bayes estimation under the two kinds of losses are verified by stochastic simulation,and the Bayes estimates under these two kinds of losses are also compared.The results show that the Bayes estimation under two kinds of losses has good estimation effect,and the Bayes estimation under entropy loss is better than those under 0-1 loss under the same sample.Finally,the Poisson difference distribution is used to empirically analyze the amount of change in the number of beds used per day in a hospital,and through the Pearson’s chi-square test,the Poisson difference distribution obtained by Bayes estimation under entropy loss fit the data better.

关 键 词：泊松差分布 BAYES估计 熵损失函数 0-1损失函数 随机模拟 

分 类 号：O212.1[理学—概率论与数理统计]