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Parameter estimation for the Pareto distribution based on ranked set sampling

  • Wenshu Qian
  • Wangxue ChenEmail author
  • Xiaofang He
Regular Article
  • 52 Downloads

Abstract

Ranked set sampling (RSS) is an efficient method for estimating parameters when exact measurement of observation is difficult and/or expensive. In the current paper, several traditional and ad hoc estimators of the scale and shape parameters \(\theta \) and \(\alpha \) from the Pareto distribution \(p(\theta ,\alpha )\) will be respectively studied in cases when one parameter is known and when both are unknown under simple random sampling, RSS and some of its modifications such as extreme RSS(ERSS) and median RSS(MRSS). It is found for estimating of \(\theta \) from \(p(\theta ,\alpha )\) in which \(\alpha \) is known, the best linear unbiased estimator (BLUE) under ERSS is more efficient than the other estimators under the other sampling techniques. For estimating of \(\alpha \) from \(p(\theta ,\alpha )\) in which \(\theta \) is known, the modified BLUE under MRSS is more efficient than the other estimators under the other sampling techniques. For estimating of \(\theta \) and \(\alpha \) from \(p(\theta ,\alpha )\) in which both are unknown, the ad hoc estimators under ERSS are more efficient than the other estimators under the other sampling techniques. All efficiencies of these estimators are simulated under imperfect ranking. A real data set is used for illustration.

Keywords

Ranked set sampling Unbiased estimator Best linear unbiased estimator Modified unbiased estimator Modified best linear unbiased estimator 

Notes

Acknowledgements

The authors thank the referees for helpful comments that have led to an improved paper.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsJishou UniversityJishouChina

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