Estimating P(Y < X) using ranked set sampling in case of the exponential distribution

H. A. Muttlak; W. A. Abu-Dayyeh; M. F. Saleh; E. Al-Sawi

doi:10.1080/03610920902912976

Estimating P(Y < X) using ranked set sampling in case of the exponential distribution

H. A. Muttlak, W. A. Abu-Dayyeh, M. F. Saleh, E. Al-Sawi

King Fahd University of Petroleum & Minerals

Research output: Contribution to journal › Article › peer-review

46 Scopus citations

Abstract

The problem of making statistical inference about θ=P(X > Y) has been under great investigation in the literature using simple random sampling (SRS) data. This problem arises naturally in the area of reliability for a system with strength X and stress Y. In this study, we will consider making statistical inference about θ using ranked set sampling (RSS) data. Several estimators are proposed to estimate θ using RSS. The properties of these estimators are investigated and compared with known estimators based on simple random sample (SRS) data. The proposed estimators based on RSS dominate those based on SRS. A motivated example using real data set is given to illustrate the computation of the newly suggested estimators.

Original language	English
Pages (from-to)	1855-1868
Number of pages	14
Journal	Communications in Statistics - Theory and Methods
Volume	39
Issue number	10
DOIs	https://doi.org/10.1080/03610920902912976
State	Published - Jun 2010

Bibliographical note

Funding Information:
The authors would like to thank the referees for their valuable comments that improved the presentation of this article. This work was supported by King Fahd University of Petroleum and Minerals, Dhahra, Saudi Arabia under the internal project #IN 2006-330.

Keywords

Efficiency
Maximum likelihood estimator
Modified maximum likelihood estimator
Ranked set sampling
Simple random sampling

ASJC Scopus subject areas

Statistics and Probability

Access to Document

10.1080/03610920902912976

Cite this

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title = "Estimating P(Y < X) using ranked set sampling in case of the exponential distribution",

abstract = "The problem of making statistical inference about θ=P(X > Y) has been under great investigation in the literature using simple random sampling (SRS) data. This problem arises naturally in the area of reliability for a system with strength X and stress Y. In this study, we will consider making statistical inference about θ using ranked set sampling (RSS) data. Several estimators are proposed to estimate θ using RSS. The properties of these estimators are investigated and compared with known estimators based on simple random sample (SRS) data. The proposed estimators based on RSS dominate those based on SRS. A motivated example using real data set is given to illustrate the computation of the newly suggested estimators.",

keywords = "Efficiency, Maximum likelihood estimator, Modified maximum likelihood estimator, Ranked set sampling, Simple random sampling",

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note = "Funding Information: The authors would like to thank the referees for their valuable comments that improved the presentation of this article. This work was supported by King Fahd University of Petroleum and Minerals, Dhahra, Saudi Arabia under the internal project \#IN 2006-330.",

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AU - Saleh, M. F.

AU - Al-Sawi, E.

N1 - Funding Information: The authors would like to thank the referees for their valuable comments that improved the presentation of this article. This work was supported by King Fahd University of Petroleum and Minerals, Dhahra, Saudi Arabia under the internal project #IN 2006-330.

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KW - Maximum likelihood estimator

KW - Modified maximum likelihood estimator

KW - Ranked set sampling

KW - Simple random sampling

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Estimating P(Y < X) using ranked set sampling in case of the exponential distribution

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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