Nonparametric confidence intervals for quantiles based on a modified ranked set sampling

A new sampling method is introduced based on the idea of the ranked set sampling scheme in which the taken samples in each set are dependent on the previous ones. Some theoretical results are presented and distribution-free confidence intervals are derived for the quantiles of any continuous population. It is shown numerically that the proposed sampling scheme may lead to 95% confidence intervals, specially for extreme quantiles, whereas they could not be found based on the ordinary ranked set sampling scheme, presented by Chen (2000) and Balakrishnan and Li (2006). Furthermore, some optimality aspects of this scheme are investigated in the sense of both coverage probability and minimum expected length. A real data set is also used to illustrate the proposed procedure. Eventually, some conclusions are stated.