Mlinex损失函数下几何分布参数的Bayes估计  

Bayesian Estimation of Geometric Distribution Parameters Under Mlinex Loss Function

作　　者：周桂兰[1] 朱宁[1] 农以宁[1] Zhou Guilan;Zhu Ning;Nong Yining(School of Mathematics and Computing Science,Guilin University of Electronic Technology,Guilin Guangxi 541004,China)

机构地区：[1]桂林电子科技大学数学与计算科学学院

出　　处：《统计与决策》2018年第19期23-28,共6页Statistics & Decision

基　　金：国家科技支撑计划课题(2015BAL04B0305);广西自然科学基金资助项目(2016GXNSFBA380102);广西科技重点研发计划项目(桂科AB16380321)

摘　　要：在Mlinex损失函数下,文章讨论了几何分布可靠度的Bayes估计问题,在可靠度的先验分布为贝塔共轭先验分布和幂分布下,得到了可靠度的Bayes估计,并证明了它的容许性。当可靠度先验分布为贝塔分布时,给出三类不同超参数的E-Bayes估计和多层Bayes估计,并在一定条件下得到E-Bayes估计、多层Bayes估计具有等价性。利用Monte Carlo数值模拟对几种估计进行比较。Under the loss function of Mlinex, this paper discusses the Bayes estimation of geometric distribution reliability.When the prior distribution of reliability is beta conjugate prior distribution and power distribution, Bayes estimation of reliability is obtained and the admissibility proved. When the prior distribution of reliability is beta distribution, the paper gives E-Bayes estimation and multi-level Bayes estimation of three different types of hyper-parameters, and under certain conditions obtains E-Bayes estimation and multi-level Bayes estimation with equivalence. Finally, the paper uses Monte Carlo numerical simulations to compare several estimates.

关 键 词：Mlinex损失函数 几何分布 BAYES估计 E-BAYES估计 多层BAYES估计 

分 类 号：O212[理学—概率论与数理统计]