Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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Nonparametric confidence intervals for quantiles based on a modified ranked set sampling

  • Morabbi, Hakime (Department of Statistics, Ferdowsi University of Mashhad) ;
  • Razmkhah, Mostafa (Department of Statistics, Ferdowsi University of Mashhad) ;
  • Ahmadi, Jafar (Department of Statistics, Ferdowsi University of Mashhad)
  • Received : 2015.08.08
  • Accepted : 2016.02.03
  • Published : 2016.03.31
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Abstract

A new sampling method is introduced based on the idea of a ranked set sampling scheme in which taken samples in each set are dependent on 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 (especially for extreme quantiles) that cannot be found based on the ordinary ranked set sampling scheme presented by Chen (2000) and Balakrishnan and Li (2006). Optimality aspects of this scheme are investigated for both coverage probability and minimum expected length criteria. A real data set is also used to illustrate the proposed procedure. Conclusions are eventually stated.

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References

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