逐步Ⅱ型删失下Burr Type X分布的参数估计  

Parameter estimation of Burr Type X distribution under progressive type II censoring

作　　者：李翠 李荣 LI Cui;LI Rong(School of Data Science and Information Engineering,Guizhou Minzu University,Guiyang 550025,China)

机构地区：[1]贵州民族大学数据科学与信息工程学院,贵州贵阳550025

出　　处：《高师理科学刊》2024年第10期13-20,共8页Journal of Science of Teachers＇College and University

基　　金：贵州省教育厅自然科学研究项目(黔教技[2022]015号);贵州省高等学校大数据分析与智能计算重点实验室项目(黔教技[2023]012号)。

摘　　要：针对逐步Ⅱ型删失数据下Burr Type X分布的参数估计问题,提出模型参数的一种新的贝叶斯估计及相应的最大后验密度(HPD)置信区间.假设伽玛分布为待估参数的先验分布,考虑待估参数的条件后验分布未知、单峰且近似对称,选取以正态分布为提议分布的Metropolis-Hastings(MH)算法生成后验样本,基于后验样本在平方误差损失函数下得到待估参数的贝叶斯估计和HPD置信区间.将基于MH算法得到的贝叶斯估计和HPD置信区间与基于EM算法得到的极大似然估计和置信区间在均方误差准则和精度意义下进行比较.Monte-Carlo模拟结果表明,基于MH算法得到的估计在均方误差准则下优于基于EM算法得到的极大似然估计,基于MH算法得到的HPD置信区间长度小于基于EM算法得到的置信区间长度.For the parameter estimation problem of the Burr Type X under progressive type II censored data,a new Bayesian estimation for model parameters and the corresponding highest posteriori density(HPD)confidence interval is proposed.Assuming that the gamma distribution is the prior distribution of the estimated parameters,and considering that the conditional posterior distribution of the estimated parameters is unknown,single-peaked and approximately symmetric,the Metropolis-Hastings(MH)algorithm with the normal distribution as the proposed distribution is selected to generate the posterior samples,so as to obtain the Bayesian estimation of the estimated parameters and the HPD confidence intervals under the squared error loss function.The Bayesian estimates and HPD confidence intervals obtained from the MH algorithm are compared with the maximum likelihood estimates and confidence intervals obtained from the EM algorithm under the mean squared error criterion and the significance of accuracy.The results of the Monte-Carlo simulation show that the estimates obtained from the MH algorithm are better than the maximum likelihood estimates obtained from the EM algorithm under the mean square error criterion,and the length of HPD confidence intervals obtained from the MH algorithm is smaller than the confidence interval obtained from the EM algorithm.

关 键 词：Burr Type X分布 逐步Ⅱ型删失 极大似然估计 贝叶斯估计 EM算法 

分 类 号：O212.1[理学—概率论与数理统计]