Abstract

Two modified ranked set sampling schemes are used to estimate the upper and lower quantiles of an underlying distribution. The performance of these sampling schemes is compared with that of ordinary ranked set sampling in view of Pitman’s measure of closeness criterion. Actually, a way of choosing estimators is proposed in the paper based on Pitman closeness which demonstrates that the mentioned modifications on ranked set sampling are useful in the problem of quantile estimation. The results are applied to the location-scale family of distributions and the Pitman closeness probabilities are obtained numerically for the cases of exponential and uniform distributions. It is shown that the proposed sampling schemes would improve the performance of the point estimators of the population quantiles specially for extreme quantiles. The proposed procedure is used to estimate the quantiles of a real data set.

摘要

两个修改后的排序集抽样方案用于估计基础分布的上分位数和下分位数。根据 Pitman 的接近度度量标准，将这些抽样方案的性能与普通排序集抽样的性能进行了比较。实际上，本文提出了一种基于 Pitman closeness 的估计量选择方法，证明了上述对排序集抽样的修改在分位数估计问题中是有用的。将结果应用于分布的位置尺度族，并在指数分布和均匀分布的情况下以数值方式获得 Pitman 接近概率。结果表明，所提出的抽样方案将提高人口分位数的点估计器的性能，特别是对于极端分位数。