Inferences for stress-strength reliability of Burr Type X distributions based on ranked set sampling

In this study, we consider the point and interval estimation of the stress-strength reliability based on ranked set sampling when the stress and the strength are both independent Burr Type X random variables. In the context of point estimation, we obtain the maximum likelihood (ML) estimator of usin...

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Published inCommunications in statistics. Simulation and computation Vol. 51; no. 6; pp. 3324 - 3340
Main Authors Akgül, Fatma Gül, Şenoğlu, Birdal
Format Journal Article
LanguageEnglish
Published Philadelphia Taylor & Francis 03.06.2022
Taylor & Francis Ltd
Subjects
Asymptotic methods
Burr Type X distribution
Confidence intervals
Efficiency
Iterative methods
Maximum likelihood estimators
Modified maximum likelihood
Random sampling
Random variables
Ranked set sampling
Reliability
Resampling
Stress-strength reliability
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Abstract In this study, we consider the point and interval estimation of the stress-strength reliability based on ranked set sampling when the stress and the strength are both independent Burr Type X random variables. In the context of point estimation, we obtain the maximum likelihood (ML) estimator of using iterative methods. We also use Mehrotra and Nanda's modified maximum likelihood methodology, which gives explicit estimator of as an alternative to the ML methodology. In view of interval estimation, we construct the asymptotic confidence interval of In addition, the bootstrap confidence intervals of are constructed based on two different resampling methods. The performance of the proposed estimators (both point and interval) is compared with their simple random sampling counterparts. A real data set from an agricultural experiment is analyzed to show the implementation of the proposed methodologies.
AbstractList In this study, we consider the point and interval estimation of the stress-strength reliability based on ranked set sampling when the stress and the strength are both independent Burr Type X random variables. In the context of point estimation, we obtain the maximum likelihood (ML) estimator of using iterative methods. We also use Mehrotra and Nanda's modified maximum likelihood methodology, which gives explicit estimator of as an alternative to the ML methodology. In view of interval estimation, we construct the asymptotic confidence interval of In addition, the bootstrap confidence intervals of are constructed based on two different resampling methods. The performance of the proposed estimators (both point and interval) is compared with their simple random sampling counterparts. A real data set from an agricultural experiment is analyzed to show the implementation of the proposed methodologies.
In this study, we consider the point and interval estimation of the stress–strength reliability based on ranked set sampling when the stress and the strength are both independent Burr Type X random variables. In the context of point estimation, we obtain the maximum likelihood (ML) estimator of using iterative methods. We also use Mehrotra and Nanda’s modified maximum likelihood methodology, which gives explicit estimator of as an alternative to the ML methodology. In view of interval estimation, we construct the asymptotic confidence interval of In addition, the bootstrap confidence intervals of are constructed based on two different resampling methods. The performance of the proposed estimators (both point and interval) is compared with their simple random sampling counterparts. A real data set from an agricultural experiment is analyzed to show the implementation of the proposed methodologies.
Author Akgül, Fatma Gül
Şenoğlu, Birdal
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  organization: Department of Computer Engineering, Artvin Çoruh University
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  givenname: Birdal
  surname: Şenoğlu
  fullname: Şenoğlu, Birdal
  organization: Department of Statistics, Ankara University
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Snippet In this study, we consider the point and interval estimation of the stress-strength reliability based on ranked set sampling when the stress and the strength...
In this study, we consider the point and interval estimation of the stress–strength reliability based on ranked set sampling when the stress and the strength...
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SubjectTerms Asymptotic methods
Burr Type X distribution
Confidence intervals
Efficiency
Iterative methods
Maximum likelihood estimators
Modified maximum likelihood
Random sampling
Random variables
Ranked set sampling
Reliability
Resampling
Stress-strength reliability
Title Inferences for stress-strength reliability of Burr Type X distributions based on ranked set sampling
URI https://www.tandfonline.com/doi/abs/10.1080/03610918.2020.1711949
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Volume 51
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