排序集抽样下指数分布参数的最优线性无偏估计  

Best Linear Unbiased Estimation of Paremeter for Exponential Distribution Based on Ranked Set Sampling

作　　者：张良勇[1] 董晓芳[1] ZHANG LIANGYONG;DONG XIAOFANG(College of Mathematics and Statistics,Hebei University of Economics and Business,Shijiazhuang 050061,China)

机构地区：[1]河北经贸大学数学与统计学学院,石家庄050061

出　　处：《应用数学学报》2022年第4期509-520,共12页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(11801134);河北省高等学校科学技术研究重点项目(ZD202062);河北经贸大学科研基金(2015KYQ03)资助项目.

摘　　要：排序集抽样方法适用于样本测量困难但排序容易的场合,其样本包含了次序信息指数分布在寿命试验中占有非常重要的地位,为了提高指数分布参数的估计效率,本文提出了排序集抽样下参数的最优线性无偏估计量,计算了新估计量的方差,证明了其具有渐近正态性相对效率和模拟效率的研究结果表明:新估计量的估计效率不仅高于简单随机抽样下一致最小方差无偏估计量,也高于排序集抽样下样本均值和修正极大似然估计量.最后,将推荐方法应用到转移性肾癌的临床研究中,从而验证该方法的有效性.The ranking set sampling method is suitable for the situation where the sample measurement is difficult blit the ranking is easy,and the sample contains the order information.Exponential distribution plays a very important role in life test.In order to improve the estimation efficiency of paremeter for exponential distribution,this paper presents the best linear unbiased estimator of paremeter under ranked set sampling,and calculates the variance of the new estimator.The new estimator is shown to have asymptotic normality.The research results of relative efficiency and simulated efficiency show that the estimation efficiency of the new estimator is not only higher than the uniformly minimum variance unbiased estimator under simple random sampling,but also higher than the sample mean and the modified maximum likelihood estimator under ranked set sampling.Finally,the proposed met hod is applied to the clinical study of metas tatic renal carcinoma to verify the effectiveness of the method.

关 键 词：排序集抽样 最优线性无偏估计 指数分布 相对效率 

分 类 号：O212.2[理学—概率论与数理统计]