Abstract

Ranked set sampling (RSS) is a method of sampling that can be advantageous when quantification of all sampling units is costly but when small sets of units can be ranked according to the character under investigation by means of visual inspection or other methods not requiring actual measurements. RSS performs better than simple random sampling (SRS) to estimate the population mean. In original RSS procedure, the units corresponding to each rank are used. In this article, we propose to use RSS method with lowest order statistics from each sample to estimate the population mean of Pareto distribution which is highly positively skew. The Pareto distribution is chosen due to its application in social and scientific phenomenon including the distribution of wealth in a society. The estimator based on lowest order statistics with bias correction term has been proposed. Two cases, known and unknown scale parameter, have been considered. The simulation-based methods have also been included. It is shown that the gains in the relative precisions of population mean based on our proposed method are uniformly higher than those based upon the RSS and extreme RSS procedures. The proposed method with bias correction term is recommended for real applications.

摘要

排名集抽样 (RSS) 是一种抽样方法，当所有抽样单位的量化成本较高，但可以通过目视检查或其他不需要实际测量的方法根据所调查的特征对小组单位进行排名时，该方法可能具有优势。在估计总体平均值方面，RSS 的性能优于简单随机抽样 (SRS)。在原始的RSS过程中，使用与每个等级相对应的单位。在本文中，我们建议使用每个样本的最低阶统计量的 RSS 方法来估计高度正偏的 Pareto 分布的总体均值。选择帕累托分布是因为它在社会和科学现象（包括社会财富分配）中的应用。提出了基于带有偏差校正项的最低阶统计量的估计器。考虑了已知和未知尺度参数两种情况。还包括基于模拟的方法。结果表明，基于我们提出的方法的总体平均相对精度的增益均高于基于 RSS 和极端 RSS 程序的增益。建议在实际应用中使用所提出的带有偏差校正项的方法。