排序集下单指数分布均值的修正极大似然估计  

Modified maximum likelihood estimator about the mean of the exponential distribution using ranked set sampling

作　　者：陈望学[1,2] 谢民育[2] 刘佳莹[2] 周焜 

机构地区：[1]吉首大学数学与统计学院,湖南吉首460000 [2]华中师范大学数学与统计学学院,武汉430079

出　　处：《华中师范大学学报（自然科学版）》2013年第6期739-742,共4页Journal of Central China Normal University：Natural Sciences

基　　金：国家自然科学基金项目(10571070)

摘　　要：排序集抽样(RSS)是一种有效的收集数据的方法.在求解RSS下单指数分布均值的极大似然估计(MLE)时,由于无法得到MLE的显性解,通常的做法是给似然方程中的后两项函数同时取均值,得到修正MLE(MMLE).该文重点考虑了仅给一项取均值,且证明了仅给一项取均值得到MMLE依然是无偏估计.数值比较表明,给一项取均值得到的MMLE方差一致小于给两项取均值得到MMLE的方差,且非常接近未修正MLE的均方差,同时小于简单随机抽样(SRS)下MLE的方差.Ranked Set Sampling（RSS） is a useful method of data collection.Since the maximum likelihood estimator（MLE） about the mean of the exponential distribution based on RSS usually has no closed expression,we usually modify likelihood equation to obtain a modified likelihood equation by replacing the latter two terms by expectation.The paper focuses on obtaining a new modified likelihood equation by replacing one term by expectation.We also prove the new modified MLE（MMLE） is a unbiased estimator and calculate its variance.Numerical results show that the variance of the new MMLE is uniformly smaller than variance of usual MMLE and is very close to the mean square error of the exact MLE.Its variance is smaller than variance of MLE using simple random sampling（SRS）.

关 键 词：排序集抽样 修正极大似然估计 无偏估计 单指数分布 

分 类 号：O212[理学—概率论与数理统计]