Parameter estimation for the Pareto distribution based on ranked set sampling

Wenshu Qian, Wangxue Chen () and Xiaofang He
Additional contact information
Wenshu Qian: Jishou University
Wangxue Chen: Jishou University
Xiaofang He: Jishou University

Statistical Papers, 2021, vol. 62, issue 1, No 16, 395-417

Abstract: 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 $$\theta $$ θ and $$\alpha $$ α from the Pareto distribution $$p(\theta ,\alpha )$$ p ( θ , α ) 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 $$\theta $$ θ from $$p(\theta ,\alpha )$$ p ( θ , α ) in which $$\alpha $$ α 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 $$\alpha $$ α from $$p(\theta ,\alpha )$$ p ( θ , α ) in which $$\theta $$ θ is known, the modified BLUE under MRSS is more efficient than the other estimators under the other sampling techniques. For estimating of $$\theta $$ θ and $$\alpha $$ α from $$p(\theta ,\alpha )$$ p ( θ , α ) 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 (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://link.springer.com/10.1007/s00362-019-01102-1 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:stpapr:v:62:y:2021:i:1:d:10.1007_s00362-019-01102-1

Ordering information: This journal article can be ordered from
http://www.springer. ... business/journal/362

DOI: 10.1007/s00362-019-01102-1

Access Statistics for this article

Statistical Papers is currently edited by C. Müller, W. Krämer and W.G. Müller

More articles in Statistical Papers from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().