优良抽样设计下~Logistic~分布中参数的极大似然估计
Maximum Likelihood Estimators of the Parameters of the Logistic Distribution Under Optimal Sampling Design
当研究目标的实际测量具有不可修复的破坏性或耗资巨大时, 有效 的抽样设计将是一项重要的研究课题. 在统计推断方面, 排序集抽样~(RSS)~被视为一种比简单随机抽样~(SRS)~更为有效的收集数据 的方式. 动态极值~RSS~(MERSS)~是一种修正的~RSS. 文章在~SRS~和~MERSS~下研 究了~Logistic~分布中参数的极大似然估计~(MLEs). 在这两种抽样下证明了该分布中位置参数和刻度参数的~MLEs~的存在性和唯一性, 并计算了所含参数的~Fisher~信息量和~Fisher~信息矩阵. 比较了这两种抽样下对应估计的渐近效率. 数值结果表明~MERSS~下的~MLEs~一致优于~SRS~下的~MLEs.
Cost effective sampling is a problem of major concern in some experiments especially when the measurement of the characteristic of interest is costly or painful or time consuming. Ranked set sampling (RSS) is now regarded as an effective tool in statistical inference and important alternative to simple random sampling (SRS). In this article, A modification of RSS called moving extremes ranked set sampling (MERSS) is considered for maximum likelihood estimators (MLEs) the parameters from the Logistic distribution. We respectively prove the existence and uniqueness of MLEs of the location parameter and the scale parameter from this distribution under SRS and MERSS. The Fisher information number and Fisher information matrix under the two sampling are respectively computed. The MLEs under MERSS are compared to the corresponding ones under SRS by the asymptotic efficiency. The simulation results show that the MLEs under MERSS are significantly more efficient than the ones under SRS.
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