Q对称熵损失下Weibull分布尺度参数的Bayes估计  

Bayes Estimation of Weibull Distribution Scale Parameters under Q-symmetric Entropy Loss

作　　者：赵孟茹 周菊玲[1] ZHAO Mengru;ZHOU Juling(School of Mathematical Sciences,Xinjiang Normal University,Urumqi 830017,China)

机构地区：[1]新疆师范大学数学科学学院,新疆乌鲁木齐830017

出　　处：《枣庄学院学报》2023年第2期21-27,共7页Journal of Zaozhuang University

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

摘　　要：在Q对称熵损失函数下,对参数的先验分布选取伽玛分布,研究Weibull分布尺度参数的Bayes估计问题。利用随机模拟,验证Weibull分布在Q对称熵损失函数下参数Bayes估计的合理性,在重复模拟下比较极大似然估计和两个Bayes估计的均方误差。结果显示,参数的Bayes估计效果更为理想,最后实例表明参数估计效果与随机模拟结论一致。Under the Q-symmetric entropy loss function,the gamma distribution is selected for the prior distribution of the parameters,and the Bayes estimation and multi-layer Bayes estimation of Weibull distribution scale parameters are studied.Through stochastic simulation,the rationality of the parameter Bayes estimation of Weibull distribution under the Q-symmetric entropy loss function is verified.The mean squared error of the maximum likelihood estimate and the two Bayes estimates ere compared under repeated simulations,and the results show that the Bayes estimation effect of the parameters is more ideal,Examples show that the parameter estimation effect is consistent with the random simulation conclusion.

关 键 词：威布尔分布 Q对称熵损失 BAYES估计 多层BAYES估计 

分 类 号：O212[理学—概率论与数理统计]