Alsadat Najwan, Hassan Amal S, Elgarhy Mohammed, Johannssen Arne, Gemeay Ahmed M
Department of Quantitative Analysis, College of Business Administration, King Saud University, P.O. Box 71115, 11587, Riyadh, Saudi Arabia.
Faculty of Graduate Studies for Statistical Research, Cairo University, 5 Dr. Ahmed Zewail Street, Giza, 12613, Egypt.
Sci Rep. 2024 Jul 31;14(1):17652. doi: 10.1038/s41598-024-67693-4.
The sample strategy employed in statistical parameter estimation issues has a major impact on the accuracy of the parameter estimates. Ranked set sampling (RSS) is a highly helpful technique for gathering data when it is difficult or impossible to quantify the units in a population. A bounded power logarithmic distribution (PLD) has been proposed recently, and it may be used to describe many real-world bounded data sets. In the current work, the three parameters of the PLD are estimated using the RSS technique. A number of conventional estimators using maximum likelihood, minimum spacing absolute log-distance, minimum spacing square distance, Anderson-Darling, minimum spacing absolute distance, maximum product of spacings, least squares, Cramer-von-Mises, minimum spacing square log distance, and minimum spacing Linex distance are investigated. The different estimates via RSS are compared with their simple random sampling (SRS) counterparts. We found that the maximum product spacing estimate appears to be the best option based on our simulation results for the SRS and RSS data sets. Estimates generated from SRS data sets are less efficient than those derived from RSS data sets. The usefulness of the RSS estimators is also investigated by means of a real data example.
统计参数估计问题中采用的抽样策略对参数估计的准确性有重大影响。当难以或无法对总体中的单位进行量化时，排序集抽样（RSS）是一种非常有用的数据收集技术。最近有人提出了有界幂对数分布（PLD），它可用于描述许多现实世界中的有界数据集。在当前工作中，使用RSS技术估计PLD的三个参数。研究了一些使用最大似然、最小间距绝对对数距离、最小间距平方距离、安德森-达林、最小间距绝对距离、最大间距乘积、最小二乘法、克拉默-冯米塞斯、最小间距平方对数距离和最小间距线性指数距离的传统估计量。将通过RSS得到的不同估计值与其简单随机抽样（SRS）对应值进行比较。基于我们对SRS和RSS数据集的模拟结果，我们发现最大间距乘积估计似乎是最佳选择。从SRS数据集生成的估计值不如从RSS数据集得出的估计值有效。还通过一个实际数据示例研究了RSS估计量的实用性。
