Optimal Confidence Regions for Weibull Parameters and Quantiles under Progressive Censoring
Confidence regions for the Weibull parameters with minimum areas among all those based on the Conditionality Principle are constructed using an equivalent diffuse Bayesian approach. The process is valid for scenarios involving standard failure and progressive censorship, and complete data. Optimal c...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-09-01
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| Series: | Algorithms |
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| Online Access: | https://www.mdpi.com/1999-4893/16/9/427 |
| _version_ | 1797581670756384768 |
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| author | Arturo J. Fernández |
| author_facet | Arturo J. Fernández |
| author_sort | Arturo J. Fernández |
| collection | DOAJ |
| description | Confidence regions for the Weibull parameters with minimum areas among all those based on the Conditionality Principle are constructed using an equivalent diffuse Bayesian approach. The process is valid for scenarios involving standard failure and progressive censorship, and complete data. Optimal conditional confidence sets for two Weibull quantiles are also derived. Simulation-based algorithms are provided for computing the smallest-area regions with fixed confidence levels. Importantly, the proposed confidence sets satisfy the Sufficiency, Likelihood and Conditionality Principles in contrast to the unconditional regions based on maximum likelihood estimators and other insufficient statistics. The suggested perspective can be applied to parametric estimation and hypothesis testing, as well as to the determination of minimum-size confidence sets for other invariantly estimable functions of the Weibull parameters. A dataset concerning failure times of an insulating fluid is studied for illustrative and comparative purposes. |
| first_indexed | 2024-03-10T23:07:51Z |
| format | Article |
| id | doaj.art-bca05942647e4066aeab990823e76b98 |
| institution | Directory Open Access Journal |
| issn | 1999-4893 |
| language | English |
| last_indexed | 2024-03-10T23:07:51Z |
| publishDate | 2023-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Algorithms |
| spelling | doaj.art-bca05942647e4066aeab990823e76b982023-11-19T09:12:59ZengMDPI AGAlgorithms1999-48932023-09-0116942710.3390/a16090427Optimal Confidence Regions for Weibull Parameters and Quantiles under Progressive CensoringArturo J. Fernández0Departamento de Matemáticas, Estadística e Investigación Operativa and Instituto de Matemáticas y Aplicaciones (IMAULL), Universidad de La Laguna (ULL), 38071 Santa Cruz de Tenerife, SpainConfidence regions for the Weibull parameters with minimum areas among all those based on the Conditionality Principle are constructed using an equivalent diffuse Bayesian approach. The process is valid for scenarios involving standard failure and progressive censorship, and complete data. Optimal conditional confidence sets for two Weibull quantiles are also derived. Simulation-based algorithms are provided for computing the smallest-area regions with fixed confidence levels. Importantly, the proposed confidence sets satisfy the Sufficiency, Likelihood and Conditionality Principles in contrast to the unconditional regions based on maximum likelihood estimators and other insufficient statistics. The suggested perspective can be applied to parametric estimation and hypothesis testing, as well as to the determination of minimum-size confidence sets for other invariantly estimable functions of the Weibull parameters. A dataset concerning failure times of an insulating fluid is studied for illustrative and comparative purposes.https://www.mdpi.com/1999-4893/16/9/427confidence and credibility regionsConditionality, Likelihood and Sufficiency PrinciplesWeibull distributionprogressively censored datareliability and life-testing |
| spellingShingle | Arturo J. Fernández Optimal Confidence Regions for Weibull Parameters and Quantiles under Progressive Censoring Algorithms confidence and credibility regions Conditionality, Likelihood and Sufficiency Principles Weibull distribution progressively censored data reliability and life-testing |
| title | Optimal Confidence Regions for Weibull Parameters and Quantiles under Progressive Censoring |
| title_full | Optimal Confidence Regions for Weibull Parameters and Quantiles under Progressive Censoring |
| title_fullStr | Optimal Confidence Regions for Weibull Parameters and Quantiles under Progressive Censoring |
| title_full_unstemmed | Optimal Confidence Regions for Weibull Parameters and Quantiles under Progressive Censoring |
| title_short | Optimal Confidence Regions for Weibull Parameters and Quantiles under Progressive Censoring |
| title_sort | optimal confidence regions for weibull parameters and quantiles under progressive censoring |
| topic | confidence and credibility regions Conditionality, Likelihood and Sufficiency Principles Weibull distribution progressively censored data reliability and life-testing |
| url | https://www.mdpi.com/1999-4893/16/9/427 |
| work_keys_str_mv | AT arturojfernandez optimalconfidenceregionsforweibullparametersandquantilesunderprogressivecensoring |