Quantile estimation based on modified ranked set sampling schemes using Pitman closeness

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.

Keywords:

• Extreme quantiles
• Location-scale family
• Order statistics
• Pitman’s measure of closeness

AMS MATHEMATICAL SUBJECT CLASSIFICATION 2010:

• Primary 62D05
• Secondary 62G05

Acknowledgements

We are very grateful to the anonymous Referees of the previous version of the paper, who suggested various modifications and changes. Their suggestions have greatly enhanced the quality of this present version.

Additional information

Funding

This research was supported by a grant from Ferdowsi University of Mashhad (No. 2/40032).