Inferential analysis of the stress-strength reliability for a new extended family of distributions
This study addresses the estimation of system reliability, denoted as [Formula: see text], where X and Y are independent but not identically distributed random variables from an extended distribution family, incorporating a new parameter to extend the normal and Weibull distributions. We propose est...
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| Format: | Article |
| Language: | English |
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Taylor & Francis
2025-12-01
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| Series: | Research in Statistics |
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| Online Access: | https://www.tandfonline.com/doi/10.1080/27684520.2025.2452926 |
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| author | Mohammed S. Kotb Mohammed Z. Raqab |
| author_facet | Mohammed S. Kotb Mohammed Z. Raqab |
| author_sort | Mohammed S. Kotb |
| collection | DOAJ |
| description | This study addresses the estimation of system reliability, denoted as [Formula: see text], where X and Y are independent but not identically distributed random variables from an extended distribution family, incorporating a new parameter to extend the normal and Weibull distributions. We propose estimators, including the maximum likelihood and Bayes estimators, as well as various confidence and credible intervals for both the unknown parameters and R, utilizing conjugate priors. In a Bayesian context, we use importance sampling within the Metropolis-Hastings sampler for parameter and reliability function estimation. Additionally, the effectiveness of our proposed methods is performed through the analysis of real-world data and comprehensive numerical simulations. |
| format | Article |
| id | doaj-art-5855b0d8df3046a796ce7a04a779b1e9 |
| institution | Kabale University |
| issn | 2768-4520 |
| language | English |
| publishDate | 2025-12-01 |
| publisher | Taylor & Francis |
| record_format | Article |
| series | Research in Statistics |
| spelling | doaj-art-5855b0d8df3046a796ce7a04a779b1e92025-02-05T13:55:22ZengTaylor & FrancisResearch in Statistics2768-45202025-12-013110.1080/27684520.2025.2452926Inferential analysis of the stress-strength reliability for a new extended family of distributionsMohammed S. Kotb0Mohammed Z. Raqab1Department of Mathematics, Al-Azhar University, Nasr City, Cairo, EgyptDepartment of Statistics & Operations Research, Kuwait University, Al-Shadadiyya, KuwaitThis study addresses the estimation of system reliability, denoted as [Formula: see text], where X and Y are independent but not identically distributed random variables from an extended distribution family, incorporating a new parameter to extend the normal and Weibull distributions. We propose estimators, including the maximum likelihood and Bayes estimators, as well as various confidence and credible intervals for both the unknown parameters and R, utilizing conjugate priors. In a Bayesian context, we use importance sampling within the Metropolis-Hastings sampler for parameter and reliability function estimation. Additionally, the effectiveness of our proposed methods is performed through the analysis of real-world data and comprehensive numerical simulations.https://www.tandfonline.com/doi/10.1080/27684520.2025.2452926Bayes estimatorconfidence intervalsmaximum likelihood estimatorMonte Carlo simulationstress-strength model |
| spellingShingle | Mohammed S. Kotb Mohammed Z. Raqab Inferential analysis of the stress-strength reliability for a new extended family of distributions Research in Statistics Bayes estimator confidence intervals maximum likelihood estimator Monte Carlo simulation stress-strength model |
| title | Inferential analysis of the stress-strength reliability for a new extended family of distributions |
| title_full | Inferential analysis of the stress-strength reliability for a new extended family of distributions |
| title_fullStr | Inferential analysis of the stress-strength reliability for a new extended family of distributions |
| title_full_unstemmed | Inferential analysis of the stress-strength reliability for a new extended family of distributions |
| title_short | Inferential analysis of the stress-strength reliability for a new extended family of distributions |
| title_sort | inferential analysis of the stress strength reliability for a new extended family of distributions |
| topic | Bayes estimator confidence intervals maximum likelihood estimator Monte Carlo simulation stress-strength model |
| url | https://www.tandfonline.com/doi/10.1080/27684520.2025.2452926 |
| work_keys_str_mv | AT mohammedskotb inferentialanalysisofthestressstrengthreliabilityforanewextendedfamilyofdistributions AT mohammedzraqab inferentialanalysisofthestressstrengthreliabilityforanewextendedfamilyofdistributions |