On the comparison of the interval estimation of the Pareto parameter under simple random sampling and ranked set sampling techniques

Aissa Omar Aissa, Kamarulzaman Ibrahim, Walid Abu Dayyeh, Wan Zawiah Wan Zin @ Wan Ibrahim

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Ranked set sampling (RSS) is recognized as a useful sampling scheme for improving the precision of the parameter estimates and increasing the efficiency of estimation. This type of scheme is appropriate when the variable of interest is expensive or time consuming to be quantified, but easy and cheap to be ranked. In this study, the estimation of the shape parameter of the Pareto distribution of the first type when the scale is known is studied for the data that are gathered under simple random sampling (SRS), RSS, and selective order statistics based on the maximum (SORSS(max)). The confidence intervals for the shape parameter of Pareto distribution under the sampling techniques considered are determined. A simulation study is carried out to compare the confidence intervals in terms of coverage probabilities (CPs) and expected lengths (ELs). When the coverage probabilities and expected lengths for the confidence intervals of the shape parameter of Pareto distribution determined based on the different sampling methods are compared, the coverage probabilities and expected lengths are found to be more precise under RSS as opposed to SRS. In particular, it is found that the coverage probabilities under SORSS(max) is closest to the nominal value of 0.95.

Original languageEnglish
Title of host publication2nd ISM International Statistical Conference 2014, ISM 2014
Subtitle of host publicationEmpowering the Applications of Statistical and Mathematical Sciences
EditorsNor Aida Zuraimi Md Noar, Roslinazairimah Zakaria, Wan Nur Syahidah Wan Yusoff, Mohd Sham Mohamad, Mohd Rashid Ab Hamid
PublisherAmerican Institute of Physics Inc.
Pages298-304
Number of pages7
ISBN (Electronic)9780735412811
DOIs
Publication statusPublished - 1 Jan 2015
Event2nd ISM International Statistical Conference 2014: Empowering the Applications of Statistical and Mathematical Sciences, ISM 2014 - Kuantan, Pahang, Malaysia
Duration: 12 Aug 201414 Aug 2014

Publication series

NameAIP Conference Proceedings
Volume1643
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616

Other

Other2nd ISM International Statistical Conference 2014: Empowering the Applications of Statistical and Mathematical Sciences, ISM 2014
CountryMalaysia
CityKuantan, Pahang
Period12/8/1414/8/14

Fingerprint

random sampling
sampling
intervals
confidence
statistics
estimates
approximation

Keywords

  • confidence intervals
  • coverage probability
  • expected length
  • Pareto distribution
  • Ranked set sampling
  • shape parameter
  • simple random sampling

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Aissa, A. O., Ibrahim, K., Dayyeh, W. A., & Wan Zin @ Wan Ibrahim, W. Z. (2015). On the comparison of the interval estimation of the Pareto parameter under simple random sampling and ranked set sampling techniques. In N. A. Z. M. Noar, R. Zakaria, W. N. S. W. Yusoff, M. S. Mohamad, & M. R. A. Hamid (Eds.), 2nd ISM International Statistical Conference 2014, ISM 2014: Empowering the Applications of Statistical and Mathematical Sciences (pp. 298-304). (AIP Conference Proceedings; Vol. 1643). American Institute of Physics Inc.. https://doi.org/10.1063/1.4907459

On the comparison of the interval estimation of the Pareto parameter under simple random sampling and ranked set sampling techniques. / Aissa, Aissa Omar; Ibrahim, Kamarulzaman; Dayyeh, Walid Abu; Wan Zin @ Wan Ibrahim, Wan Zawiah.

2nd ISM International Statistical Conference 2014, ISM 2014: Empowering the Applications of Statistical and Mathematical Sciences. ed. / Nor Aida Zuraimi Md Noar; Roslinazairimah Zakaria; Wan Nur Syahidah Wan Yusoff; Mohd Sham Mohamad; Mohd Rashid Ab Hamid. American Institute of Physics Inc., 2015. p. 298-304 (AIP Conference Proceedings; Vol. 1643).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Aissa, AO, Ibrahim, K, Dayyeh, WA & Wan Zin @ Wan Ibrahim, WZ 2015, On the comparison of the interval estimation of the Pareto parameter under simple random sampling and ranked set sampling techniques. in NAZM Noar, R Zakaria, WNSW Yusoff, MS Mohamad & MRA Hamid (eds), 2nd ISM International Statistical Conference 2014, ISM 2014: Empowering the Applications of Statistical and Mathematical Sciences. AIP Conference Proceedings, vol. 1643, American Institute of Physics Inc., pp. 298-304, 2nd ISM International Statistical Conference 2014: Empowering the Applications of Statistical and Mathematical Sciences, ISM 2014, Kuantan, Pahang, Malaysia, 12/8/14. https://doi.org/10.1063/1.4907459
Aissa AO, Ibrahim K, Dayyeh WA, Wan Zin @ Wan Ibrahim WZ. On the comparison of the interval estimation of the Pareto parameter under simple random sampling and ranked set sampling techniques. In Noar NAZM, Zakaria R, Yusoff WNSW, Mohamad MS, Hamid MRA, editors, 2nd ISM International Statistical Conference 2014, ISM 2014: Empowering the Applications of Statistical and Mathematical Sciences. American Institute of Physics Inc. 2015. p. 298-304. (AIP Conference Proceedings). https://doi.org/10.1063/1.4907459
Aissa, Aissa Omar ; Ibrahim, Kamarulzaman ; Dayyeh, Walid Abu ; Wan Zin @ Wan Ibrahim, Wan Zawiah. / On the comparison of the interval estimation of the Pareto parameter under simple random sampling and ranked set sampling techniques. 2nd ISM International Statistical Conference 2014, ISM 2014: Empowering the Applications of Statistical and Mathematical Sciences. editor / Nor Aida Zuraimi Md Noar ; Roslinazairimah Zakaria ; Wan Nur Syahidah Wan Yusoff ; Mohd Sham Mohamad ; Mohd Rashid Ab Hamid. American Institute of Physics Inc., 2015. pp. 298-304 (AIP Conference Proceedings).
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