Estimation and Bayesian Prediction of the Generalized Pareto Distribution in the Context of a Progressive Type-II Censoring Scheme
The generalized Pareto distribution plays a significant role in reliability research. This study concentrates on the statistical inference of the generalized Pareto distribution utilizing progressively Type-II censored data. Estimations are performed using maximum likelihood estimation through the e...
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MDPI AG
2024-09-01
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| author | Tianrui Ye Wenhao Gui |
| author_facet | Tianrui Ye Wenhao Gui |
| author_sort | Tianrui Ye |
| collection | DOAJ |
| description | The generalized Pareto distribution plays a significant role in reliability research. This study concentrates on the statistical inference of the generalized Pareto distribution utilizing progressively Type-II censored data. Estimations are performed using maximum likelihood estimation through the expectation–maximization approach. Confidence intervals are derived using the asymptotic confidence intervals. Bayesian estimations are conducted using the Tierney and Kadane method alongside the Metropolis–Hastings algorithm, and the highest posterior density credible interval estimation is accomplished. Furthermore, Bayesian predictive intervals and future sample estimations are explored. To illustrate these inference techniques, a simulation and practical example are presented for analysis. |
| format | Article |
| id | doaj-art-5be51d741e514150af3b4f2bb3b61a30 |
| institution | OA Journals |
| issn | 2076-3417 |
| language | English |
| publishDate | 2024-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Applied Sciences |
| spelling | doaj-art-5be51d741e514150af3b4f2bb3b61a302025-08-20T01:55:58ZengMDPI AGApplied Sciences2076-34172024-09-011418843310.3390/app14188433Estimation and Bayesian Prediction of the Generalized Pareto Distribution in the Context of a Progressive Type-II Censoring SchemeTianrui Ye0Wenhao Gui1Department of Statistics and Operations Research, University of North Carolina, Chapel Hill, NC 27599, USASchool of Mathematics and Statistics, Beijing Jiaotong University, Beijing 100044, ChinaThe generalized Pareto distribution plays a significant role in reliability research. This study concentrates on the statistical inference of the generalized Pareto distribution utilizing progressively Type-II censored data. Estimations are performed using maximum likelihood estimation through the expectation–maximization approach. Confidence intervals are derived using the asymptotic confidence intervals. Bayesian estimations are conducted using the Tierney and Kadane method alongside the Metropolis–Hastings algorithm, and the highest posterior density credible interval estimation is accomplished. Furthermore, Bayesian predictive intervals and future sample estimations are explored. To illustrate these inference techniques, a simulation and practical example are presented for analysis.https://www.mdpi.com/2076-3417/14/18/8433generalized Pareto distributionexpectation–maximization algorithmprogressive Type-II censoringMetropolis–Hasting approachBayesian estimationBayesian prediction |
| spellingShingle | Tianrui Ye Wenhao Gui Estimation and Bayesian Prediction of the Generalized Pareto Distribution in the Context of a Progressive Type-II Censoring Scheme Applied Sciences generalized Pareto distribution expectation–maximization algorithm progressive Type-II censoring Metropolis–Hasting approach Bayesian estimation Bayesian prediction |
| title | Estimation and Bayesian Prediction of the Generalized Pareto Distribution in the Context of a Progressive Type-II Censoring Scheme |
| title_full | Estimation and Bayesian Prediction of the Generalized Pareto Distribution in the Context of a Progressive Type-II Censoring Scheme |
| title_fullStr | Estimation and Bayesian Prediction of the Generalized Pareto Distribution in the Context of a Progressive Type-II Censoring Scheme |
| title_full_unstemmed | Estimation and Bayesian Prediction of the Generalized Pareto Distribution in the Context of a Progressive Type-II Censoring Scheme |
| title_short | Estimation and Bayesian Prediction of the Generalized Pareto Distribution in the Context of a Progressive Type-II Censoring Scheme |
| title_sort | estimation and bayesian prediction of the generalized pareto distribution in the context of a progressive type ii censoring scheme |
| topic | generalized Pareto distribution expectation–maximization algorithm progressive Type-II censoring Metropolis–Hasting approach Bayesian estimation Bayesian prediction |
| url | https://www.mdpi.com/2076-3417/14/18/8433 |
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