Estimation of the scale parameter of a log-logistic distribution
Estimation of the scale parameter of a log-logistic distribution
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DOI：
10.1007/s00184-012-0397-5
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发表时间：
2012-05
期刊：
影响因子：
0.7
通讯作者：
G. Lesitha;P. Yageen Thomas
中科院分区：
文献类型：
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作者：
G. Lesitha;P. Yageen Thomas
本文应用秩集抽样技术，在样本中的单位可以用判断法排序而无误差的情况下，估计了对数-Logistic分布的尺度参数。我们已经评估了Fisher信息中所包含的顺序统计量所产生的这种分布，并观察到，中位数的随机样本包含的最大信息的参数。因此，我们使用中位数排序集抽样进行估计。我们进一步进行了多级中位数排序集抽样，以提高估计精度。假设不可能按照无误差的判断方法对样本中的单位进行排序，但可以根据Morgenstern型二元对数逻辑分布（MTBLLD）等辅助变量对单位进行排序。在这种情况下，我们从MTBLLD中导出了随机样本的r阶统计量伴随中所含的Fisher信息，并确定了其中具有最大Fisher信息量的伴随，利用样本中的这些单位定义了一个不平衡的秩集抽样，从而提出了一个利用秩集样本中这些单位的测量值的估计量。
In this work the ranked set sampling technique has been applied to estimate the scale parameterof a log-logistic distribution under a situation where the units in a sample can be ordered by judgement method without any error. We have evaluated the Fisher information contained in the order statistics arising from this distribution and observed that median of a random sample contains the maximum information about the parameter. Accordingly we have used median ranked set sampling to estimate. We have further carried out the multistage median ranked set sampling to estimatewith improved precision. Suppose it is not possible to rank the units in a sample according to judgement method without error but the units can be ordered based on an auxiliary variablesuch thathas a Morgenstern type bivariate log-logistic distribution (MTBLLD). In such a situation we have derived the Fisher information contained in the concomitant of rth order statistic of a random sample of sizefrom MTBLLD and identified those concomitants among others which possess largest amount of Fisher information and defined an unbalanced ranked set sampling utilizing those units in the sample and thereby proposed an estimator ofusing the measurements made on those units in this ranked set sample.