Bilal分布中参数的修正极大似然估计及其抽样性质  

Modified Maximum Likelihood Estimator and Sampling Properties of Estimator for Bilal Distribution

作　　者：汪寒 陈望学[1] WANG Han;CHEN Wangxue(College of Mathematics and Statistics,Jishou University,Jishou 416000)

机构地区：[1]吉首大学数学与统计学院,吉首416000

出　　处：《系统科学与数学》2025年第2期639-650,共12页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(12261036,11901236);湖南省自然科学面上基金项目(2022JJ30469);湖南省教育厅重点项目(21A0328);2020年湖南省教学改革项目(HNJG-2020-0552);2022年湖南省学位与研究生教学改革研究项目(2022JGZD051)资助课题。

摘　　要：Bilal分布作为寿命模型,在生存分析中起着重要作用.文章分别在简单随机抽样(SRS)和排序集抽样(RSS)下研究了Bilal分布中参数θ的修正极大似然估计(MLE),获得了该修正MLE的有限样本性质和大样本性质.数值结果表明,同等样本容量下的RSS修正MLE比SRS修正MLE有效.数值模拟也显示同种抽样下MLE的均方误差和修正MLE的方差是非常接近的,但具有显性解的修正MLE在实际中使用更方便.Bilal distribution is the most exploited distribution for life-time data analysis.In this paper,we study the modified maximum likelihood estimator(MLE)of the parameter for Bilal distribution under simple random sampling(SRS)and ranked set sampling(RSS)and obtain finite sample properties and large sample properties of the modified MLE.Numerical results show that modified MLE under RSS can be real competitors against the ones based on SRS,when the sample size is used.Numerical results also show that the mean square error of classical MLE is very close to the variance of modified MLE under the same sampling,but modified MLE with explicit solution is more convenient to use in practice.

关 键 词：排序集抽样 修正极大似然估计 有限样本性质 大样本性质 

分 类 号：O212.1[理学—概率论与数理统计]