熵损失下产品可靠度的E_Bayes估计  

Expected Bayesian Estimation of Product Reliability under Entropy Loss Function

作　　者：许道军 费时龙[2] 潘保国 XU Daojun;FEI Shilong;PAN Baoguo(Basic Department,Army Artillery and Air Defense Academy,Hefei 230031,China;School of Mathematics&Statistics,Suzhou University,Suzhou 234000,China)

机构地区：[1]陆军炮兵防空兵学院基础部,安徽合肥230031 [2]宿州学院数学与统计学院,安徽宿州234000

出　　处：《贵州大学学报（自然科学版）》2020年第1期10-13,18,共5页Journal of Guizhou University:Natural Sciences

基　　金：安徽省高等学校省级自然科学基金项目资助(KJ2016A770);陆军炮兵防空兵学院自主立项基金项目资助

摘　　要：研究了熵损失下产品可靠度的E_Bayes估计及其性质。提出了一种新的参数估计方法--E_Bayes估计法。在熵损失函数下,分别就超参数的不同先验分布,给出产品可靠度的E_Bayes估计及其性质,并通过实例将可靠度的E_Bayes估计与多层Bayes估计进行比较。可靠度的E_Bayes估计避免了多层Bayes估计复杂的积分计算,形式上更加简洁,便于计算。对于同一组数据,可靠度的E_Bayes估计和多层Bayes估计的数值计算结果十分接近。可靠度的E_Bayes估计不仅具有多层Bayes估计的稳健性,而且具有多层Bayes估计的精确性,应用更加方便,表明可靠度的E_Bayes估计法是可行的。The expected Bayesian estimation and its properties for product reliability under entropy loss function were studied.The expected Bayesian estimation was defined,which is based on the Bayesian estimation.The expected Bayesian estimation and the hierarchical Bayesian estimation of product reliability were estimated after the prior distribution of super parameters were given.Furthermore,the properties of expected Bayesian estimation were proved.Finally,calculation was performed regarding to practical problem.The results indicate that the expected Bayesian estimation can effectively avoid the complexed integral of the hierarchical Bayesian estimation,and the expected Bayesian estimation is more concise and more convenient to calculate.The expected Bayesian estimation and the hierarchical Bayesian estimation for the Reliability are not only both steady but also approximative.As a conclusion,we get that the expected Bayesian estimation method is more feasible and easier to operate.

关 键 词：二项分布 可靠度 熵损失 E_Bayes估计 多层BAYES估计 

分 类 号：O213.2[理学—概率论与数理统计]