Bayesian and Frequentist Estimation of Stress-Strength Reliability from a New Extended Burr XII Distribution
In this article, we propose and study a new three-parameter heavy-tailed distribution that unifes the Burr type XII and power inverted Topp-Leone distributions in an original manner. This unification is made through the use of a simple 'shift parameter'. Among its interesting functionalit...
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Instituto Nacional de Estatística | Statistics Portugal
2025-02-01
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| Series: | Revstat Statistical Journal |
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| Online Access: | https://revstat.ine.pt/index.php/REVSTAT/article/view/544 |
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| author | Varun Agiwal Shikhar Tyagi Christophe Chesneau |
| author_facet | Varun Agiwal Shikhar Tyagi Christophe Chesneau |
| author_sort | Varun Agiwal |
| collection | DOAJ |
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In this article, we propose and study a new three-parameter heavy-tailed distribution that unifes the Burr type XII and power inverted Topp-Leone distributions in an original manner. This unification is made through the use of a simple 'shift parameter'. Among its interesting functionalities, it exhibits possibly decreasing and unimodal probability density and hazard rate functions. We examine its quantile function, stochastic dominance, ordinary moments, weighted moments, incomplete moments, and stress-strength reliability cofficient. Then, the classical and Bayesian approaches are developed to estimate the model and stress strength reliability parameters. Bayes estimates are obtained under the squared error and entropy loss functions. Simulated data are considered to point out the performance of the derived estimates based on the mean squared error. In the final part, the potential of the new model is exemplified by the analysis of two engineering data sets, showing that it is preferable to other reputable and comparable models.
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| format | Article |
| id | doaj-art-e30b80ade3f1401691be271befd39ad4 |
| institution | Kabale University |
| issn | 1645-6726 2183-0371 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | Instituto Nacional de Estatística | Statistics Portugal |
| record_format | Article |
| series | Revstat Statistical Journal |
| spelling | doaj-art-e30b80ade3f1401691be271befd39ad42025-02-06T10:52:38ZengInstituto Nacional de Estatística | Statistics PortugalRevstat Statistical Journal1645-67262183-03712025-02-0123110.57805/revstat.v23i1.544Bayesian and Frequentist Estimation of Stress-Strength Reliability from a New Extended Burr XII DistributionVarun Agiwal0Shikhar Tyagi1Christophe Chesneau 2Indian Institute of Public HealthChrist Deemed to be UniversityUniversité de Caen-Normandie In this article, we propose and study a new three-parameter heavy-tailed distribution that unifes the Burr type XII and power inverted Topp-Leone distributions in an original manner. This unification is made through the use of a simple 'shift parameter'. Among its interesting functionalities, it exhibits possibly decreasing and unimodal probability density and hazard rate functions. We examine its quantile function, stochastic dominance, ordinary moments, weighted moments, incomplete moments, and stress-strength reliability cofficient. Then, the classical and Bayesian approaches are developed to estimate the model and stress strength reliability parameters. Bayes estimates are obtained under the squared error and entropy loss functions. Simulated data are considered to point out the performance of the derived estimates based on the mean squared error. In the final part, the potential of the new model is exemplified by the analysis of two engineering data sets, showing that it is preferable to other reputable and comparable models. https://revstat.ine.pt/index.php/REVSTAT/article/view/544Burr distributionBayesian inferenceMaximum likelihood methodstress-strength reliabilitydata analysis |
| spellingShingle | Varun Agiwal Shikhar Tyagi Christophe Chesneau Bayesian and Frequentist Estimation of Stress-Strength Reliability from a New Extended Burr XII Distribution Revstat Statistical Journal Burr distribution Bayesian inference Maximum likelihood method stress-strength reliability data analysis |
| title | Bayesian and Frequentist Estimation of Stress-Strength Reliability from a New Extended Burr XII Distribution |
| title_full | Bayesian and Frequentist Estimation of Stress-Strength Reliability from a New Extended Burr XII Distribution |
| title_fullStr | Bayesian and Frequentist Estimation of Stress-Strength Reliability from a New Extended Burr XII Distribution |
| title_full_unstemmed | Bayesian and Frequentist Estimation of Stress-Strength Reliability from a New Extended Burr XII Distribution |
| title_short | Bayesian and Frequentist Estimation of Stress-Strength Reliability from a New Extended Burr XII Distribution |
| title_sort | bayesian and frequentist estimation of stress strength reliability from a new extended burr xii distribution |
| topic | Burr distribution Bayesian inference Maximum likelihood method stress-strength reliability data analysis |
| url | https://revstat.ine.pt/index.php/REVSTAT/article/view/544 |
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