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.

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