Bayesian Estimation of the Stress-Strength Reliability Based on Generalized Order Statistics for Pareto Distribution
The aim of this paper is to obtain a Bayesian estimator of stress-strength reliability based on generalized order statistics for Pareto distribution. The dependence of the Pareto distribution support on the parameter complicates the calculations. Hence, in literature, one of the parameters is assume...
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| Format: | Article |
| Language: | English |
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Wiley
2023-01-01
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| Series: | Journal of Probability and Statistics |
| Online Access: | http://dx.doi.org/10.1155/2023/8648261 |
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| _version_ | 1832559620800905216 |
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| author | Zahra Karimi Ezmareh Gholamhossein Yari |
| author_facet | Zahra Karimi Ezmareh Gholamhossein Yari |
| author_sort | Zahra Karimi Ezmareh |
| collection | DOAJ |
| description | The aim of this paper is to obtain a Bayesian estimator of stress-strength reliability based on generalized order statistics for Pareto distribution. The dependence of the Pareto distribution support on the parameter complicates the calculations. Hence, in literature, one of the parameters is assumed to be known. In this paper, for the first time, two parameters of Pareto distribution are considered unknown. In computing the Bayesian confidence interval for reliability based on generalized order statistics, the posterior distribution has a complex form that cannot be sampled by conventional methods. To solve this problem, we propose an acceptance-rejection algorithm to generate a sample of the posterior distribution. We also propose a particular case of this model and obtain the classical and Bayesian estimators for this particular case. In this case, to obtain the Bayesian estimator of stress-strength reliability, we propose a variable change method. Then, these confidence intervals are compared by simulation. Finally, a practical example of this study is provided. |
| format | Article |
| id | doaj-art-514dde577402430a92cdd55081505125 |
| institution | Kabale University |
| issn | 1687-9538 |
| language | English |
| publishDate | 2023-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Probability and Statistics |
| spelling | doaj-art-514dde577402430a92cdd550815051252025-02-03T01:29:35ZengWileyJournal of Probability and Statistics1687-95382023-01-01202310.1155/2023/8648261Bayesian Estimation of the Stress-Strength Reliability Based on Generalized Order Statistics for Pareto DistributionZahra Karimi Ezmareh0Gholamhossein Yari1Iran University of Science & TechnologyIran University of Science & TechnologyThe aim of this paper is to obtain a Bayesian estimator of stress-strength reliability based on generalized order statistics for Pareto distribution. The dependence of the Pareto distribution support on the parameter complicates the calculations. Hence, in literature, one of the parameters is assumed to be known. In this paper, for the first time, two parameters of Pareto distribution are considered unknown. In computing the Bayesian confidence interval for reliability based on generalized order statistics, the posterior distribution has a complex form that cannot be sampled by conventional methods. To solve this problem, we propose an acceptance-rejection algorithm to generate a sample of the posterior distribution. We also propose a particular case of this model and obtain the classical and Bayesian estimators for this particular case. In this case, to obtain the Bayesian estimator of stress-strength reliability, we propose a variable change method. Then, these confidence intervals are compared by simulation. Finally, a practical example of this study is provided.http://dx.doi.org/10.1155/2023/8648261 |
| spellingShingle | Zahra Karimi Ezmareh Gholamhossein Yari Bayesian Estimation of the Stress-Strength Reliability Based on Generalized Order Statistics for Pareto Distribution Journal of Probability and Statistics |
| title | Bayesian Estimation of the Stress-Strength Reliability Based on Generalized Order Statistics for Pareto Distribution |
| title_full | Bayesian Estimation of the Stress-Strength Reliability Based on Generalized Order Statistics for Pareto Distribution |
| title_fullStr | Bayesian Estimation of the Stress-Strength Reliability Based on Generalized Order Statistics for Pareto Distribution |
| title_full_unstemmed | Bayesian Estimation of the Stress-Strength Reliability Based on Generalized Order Statistics for Pareto Distribution |
| title_short | Bayesian Estimation of the Stress-Strength Reliability Based on Generalized Order Statistics for Pareto Distribution |
| title_sort | bayesian estimation of the stress strength reliability based on generalized order statistics for pareto distribution |
| url | http://dx.doi.org/10.1155/2023/8648261 |
| work_keys_str_mv | AT zahrakarimiezmareh bayesianestimationofthestressstrengthreliabilitybasedongeneralizedorderstatisticsforparetodistribution AT gholamhosseinyari bayesianestimationofthestressstrengthreliabilitybasedongeneralizedorderstatisticsforparetodistribution |