Analysis of unit-Weibull based on progressive type-II censored with optimal scheme
Using progressive Type-II censoring data, this study deals with the estimation of parameters of the Unit-Weibull distribution using two classical methods and the Bayesian method. In the classical methods, maximum likelihood and the maximum product of spacing (MPS) methods are used to obtain the para...
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| Format: | Article |
| Language: | English |
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Elsevier
2023-01-01
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| Series: | Alexandria Engineering Journal |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S111001682200521X |
| _version_ | 1797943128930385920 |
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| author | Ehab M. Almetwally Taghreed M. Jawa Neveen Sayed-Ahmed Choonkil Park Mohammed Zakarya Sanku Dey |
| author_facet | Ehab M. Almetwally Taghreed M. Jawa Neveen Sayed-Ahmed Choonkil Park Mohammed Zakarya Sanku Dey |
| author_sort | Ehab M. Almetwally |
| collection | DOAJ |
| description | Using progressive Type-II censoring data, this study deals with the estimation of parameters of the Unit-Weibull distribution using two classical methods and the Bayesian method. In the classical methods, maximum likelihood and the maximum product of spacing (MPS) methods are used to obtain the parameters of the model by utilizing the Newton–Raphson method. On the basis of observed Fisher information matrix, approximate confidence intervals for the unknown parameters are obtained. In addition, two bootstrap methods are used to obtain confidence intervals for the unknown parameters of the model. In the Bayesian estimation, we have considered both likelihood function as well as product of spacing function to estimate the model parameters. Bayes estimators are obtained under squared error loss function using independent gamma density priors for the unknown model parameters. Since closed-form of the Bayes estimators is not available, the Metropolis–Hastings algorithm is proposed to approximate the Bayes estimates. In addition, highest posterior density credible intervals are obtained. Further, using different optimally criteria, an optimal scheme has been proposed. A simulation study is conducted to assess the statistical performance of all the estimators. To demonstrate the proposed methodology a real data analysis is provided to illustrate all the statistical inferential procedures developed in the paper. |
| first_indexed | 2024-04-10T20:19:25Z |
| format | Article |
| id | doaj.art-f12b39b3d10c4c3a8e9846bd9664ab5a |
| institution | Directory Open Access Journal |
| issn | 1110-0168 |
| language | English |
| last_indexed | 2024-04-10T20:19:25Z |
| publishDate | 2023-01-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Alexandria Engineering Journal |
| spelling | doaj.art-f12b39b3d10c4c3a8e9846bd9664ab5a2023-01-26T04:44:21ZengElsevierAlexandria Engineering Journal1110-01682023-01-0163321338Analysis of unit-Weibull based on progressive type-II censored with optimal schemeEhab M. Almetwally0Taghreed M. Jawa1Neveen Sayed-Ahmed2Choonkil Park3Mohammed Zakarya4Sanku Dey5Faculty of Business Administration, Delta University of Science and Technology, Gamasa 11152, Egypt; The Scientific Association for Studies and Applied Research (SASAR), Al Manzalah, Egypt; Corresponding authors at: Faculty of Business Administration, Delta University of Science and Technology, Gamasa 11152, Egypt (E. M. Almetwally) and Research Institute for Natural Sciences, Hanyang University, Seoul 04763, Republic of Korea (C. Park).Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi ArabiaDepartment of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi ArabiaResearch Institute for Natural Sciences, Hanyang University, Seoul 04763, Republic of Korea; Corresponding authors at: Faculty of Business Administration, Delta University of Science and Technology, Gamasa 11152, Egypt (E. M. Almetwally) and Research Institute for Natural Sciences, Hanyang University, Seoul 04763, Republic of Korea (C. Park).Department of Mathematics, College of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi Arabia; Department of Mathematics, Faculty of Science, Al-Azhar University, 71524 Assiut, EgyptDepartment of Statistics, St. Anthony’s College, Shillong, Meghalaya, IndiaUsing progressive Type-II censoring data, this study deals with the estimation of parameters of the Unit-Weibull distribution using two classical methods and the Bayesian method. In the classical methods, maximum likelihood and the maximum product of spacing (MPS) methods are used to obtain the parameters of the model by utilizing the Newton–Raphson method. On the basis of observed Fisher information matrix, approximate confidence intervals for the unknown parameters are obtained. In addition, two bootstrap methods are used to obtain confidence intervals for the unknown parameters of the model. In the Bayesian estimation, we have considered both likelihood function as well as product of spacing function to estimate the model parameters. Bayes estimators are obtained under squared error loss function using independent gamma density priors for the unknown model parameters. Since closed-form of the Bayes estimators is not available, the Metropolis–Hastings algorithm is proposed to approximate the Bayes estimates. In addition, highest posterior density credible intervals are obtained. Further, using different optimally criteria, an optimal scheme has been proposed. A simulation study is conducted to assess the statistical performance of all the estimators. To demonstrate the proposed methodology a real data analysis is provided to illustrate all the statistical inferential procedures developed in the paper.http://www.sciencedirect.com/science/article/pii/S111001682200521XProgressive Type-II censoringBayes estimatorBootstrappingMetropolis-Hasting algorithmoptimality |
| spellingShingle | Ehab M. Almetwally Taghreed M. Jawa Neveen Sayed-Ahmed Choonkil Park Mohammed Zakarya Sanku Dey Analysis of unit-Weibull based on progressive type-II censored with optimal scheme Alexandria Engineering Journal Progressive Type-II censoring Bayes estimator Bootstrapping Metropolis-Hasting algorithm optimality |
| title | Analysis of unit-Weibull based on progressive type-II censored with optimal scheme |
| title_full | Analysis of unit-Weibull based on progressive type-II censored with optimal scheme |
| title_fullStr | Analysis of unit-Weibull based on progressive type-II censored with optimal scheme |
| title_full_unstemmed | Analysis of unit-Weibull based on progressive type-II censored with optimal scheme |
| title_short | Analysis of unit-Weibull based on progressive type-II censored with optimal scheme |
| title_sort | analysis of unit weibull based on progressive type ii censored with optimal scheme |
| topic | Progressive Type-II censoring Bayes estimator Bootstrapping Metropolis-Hasting algorithm optimality |
| url | http://www.sciencedirect.com/science/article/pii/S111001682200521X |
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