ABSTRACT In statistical parameter estimation problems, how well the parameters are estimated largely depends on the sampling design used. In this article, a modified best linear unbiased estimator of the shape parameter β from log-logistic distribution is considered when scale parameter α is known and when α is unknown under simple random sampling (SRS) and ranked set sampling (RSS). In addition, a modified BLUE of β, when α is known using an RSS version based on the order statistic that maximizes the Fisher information for a fixed set size, will be considered. Theoretical properties of the suggested estimators are compared with its counterpart estimators under SRS. It is found that these estimators under RSS can be real competitors against those under SRS.

中文翻译：

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对数逻辑分布形状参数的修正最佳线性无偏估计量

摘要 在统计参数估计问题中，参数估计的好坏很大程度上取决于所使用的抽样设计。在本文中，在简单随机抽样 (SRS) 和排序集抽样 (RSS) 下，当尺度参数 α 已知且 α 未知时，考虑了对数逻辑分布的形状参数 β 的改进的最佳线性无偏估计器。此外，当使用 RSS 版本已知 α 时，β 的修正 BLUE 将被考虑，该版本基于使固定集大小的 Fisher 信息最大化的顺序统计。将建议的估计量的理论性质与 SRS 下的对应估计量进行比较。发现RSS下的这些估计量可以与SRS下的估计量真正竞争。