Hassan Amal S, Atia Samah A
Faculty of Graduate Studies for Statistical Research, Cairo University, Giza, 12613, Egypt.
Sci Rep. 2024 Oct 26;14(1):25450. doi: 10.1038/s41598-024-74468-4.
A very useful modification to ranked set sampling (RSS) that allows a larger set size without significantly increasing ranking errors is the maximum ranked set sampling with unequal samples (MRSSU) approach. This article covers the parameter estimation of the inverted Kumaraswamy distribution using MRSSU and RSS designs. The maximum likelihood and Bayesian estimation techniques are considered. The regarded Bayesian estimation technique is determined in the case of non-informative and informative priors represented by Jeffreys and gamma priors, respectively. Squared error and minimum expected are the two loss functions that are employed. We presented a simulation study to evaluate the performance of the recommended estimations using root mean squared error and relative bias. The Bayes point estimates were computed using the Metropolis-Hastings algorithm. Additional conclusions have been made based on actual geological data regarding the intervals between Kiama Blowhole's 64 consecutive eruptions. Based on the same number of measured units, the results of simulation and real data analysis showed that MRSSU estimators performed much better than their RSS counterparts.
对有序集抽样（RSS）的一种非常有用的改进是不等样本最大有序集抽样（MRSSU）方法，它允许更大的样本集大小，而不会显著增加排序误差。本文涵盖了使用MRSSU和RSS设计对逆Kumaraswamy分布进行参数估计的内容。考虑了最大似然估计和贝叶斯估计技术。所考虑的贝叶斯估计技术分别在由Jeffreys先验和伽马先验表示的非信息先验和信息先验的情况下确定。采用平方误差和最小期望作为两个损失函数。我们进行了一项模拟研究，以使用均方根误差和相对偏差来评估推荐估计量的性能。贝叶斯点估计使用Metropolis-Hastings算法进行计算。基于关于基亚马气孔64次连续喷发间隔的实际地质数据得出了其他结论。基于相同数量的测量单元，模拟和实际数据分析结果表明，MRSSU估计量的性能远优于其RSS对应估计量。
