Environmental and Ecological Statistics

, Volume 25, Issue 2, pp 237–256 | Cite as

Randomly selected order statistics in ranked set sampling: A less expensive comparable alternative to simple random sampling

  • Saeid Amiri
  • Mohammad Jafari Jozani
  • Reza ModarresEmail author


Rank-based sampling designs are powerful alternatives to simple random sampling (SRS) and often provide large improvements in the precision of estimators. In many environmental, ecological, agricultural, industrial and/or medical applications the interest lies in sampling designs that are cheaper than SRS and provide comparable estimates. In this paper, we propose a new variation of ranked set sampling (RSS) for estimating the population mean based on the random selection technique to measure a smaller number of observations than RSS design. We study the properties of the population mean estimator using the proposed design and provide conditions under which the mean estimator performs better than SRS and some existing rank-based sampling designs. Theoretical results are augmented with some numerical studies and a real-life example, where we also study the performance of our proposed design under perfect and imperfect ranking situations.


Mean estimation Order statistics Random selection Ranked set sampling 



We would like to thank the constructive comments by two anonymous referees and an associate editor which improved the quality and the presentation of our results. Mohammad Jafari Jozani gratefully acknowledges the research support of NSERC (Natural Sciences and Engineering Research Council of Canada).


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Saeid Amiri
    • 1
  • Mohammad Jafari Jozani
    • 2
  • Reza Modarres
    • 3
    Email author
  1. 1.Department of Natural and Applied SciencesUniversity of Wisconsin-Green BayGreen BayUSA
  2. 2.Department of StatisticsUniversity of ManitobaWinnipegCanada
  3. 3.Department of StatisticsThe George Washington UniversityWashingtonUSA

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