Inferences for the Change-Point of The Exponentiated Weibull Hazard Function
In many applications of lifetime data analysis, it is important to perform inferences about the change-point of the hazard function. The change-point could be a maximum for unimodal hazard functions or a minimum for bathtub forms of hazard functions and is usually of great interest in medical or in...
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| Format: | Article |
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Instituto Nacional de Estatística | Statistics Portugal
2012-11-01
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| Series: | Revstat Statistical Journal |
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| Online Access: | https://revstat.ine.pt/index.php/REVSTAT/article/view/121 |
| _version_ | 1828357075265126400 |
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| author | Josmar Mazucheli Emílio Augusto Coelho-Barros |
| author_facet | Josmar Mazucheli Emílio Augusto Coelho-Barros |
| author_sort | Josmar Mazucheli |
| collection | DOAJ |
| description |
In many applications of lifetime data analysis, it is important to perform inferences about the change-point of the hazard function. The change-point could be a maximum for unimodal hazard functions or a minimum for bathtub forms of hazard functions and is usually of great interest in medical or industrial applications. For lifetime distributions where this change-point of the hazard function can be analytically calculated, its maximum likelihood estimator is easily obtained from the invariance properties of the maximum likelihood estimators. From the asymptotical normality of the maximum likelihood estimators, confidence intervals can also be obtained. Considering the exponentiated Weibull distribution for the lifetime data, we have different forms for the hazard function: constant, increasing, unimodal, decreasing or bathtub forms. This model gives great flexibility of fit, but we do not have analytic expressions for the change-point of the hazard function. In this way, we consider the use of Markov Chain Monte Carlo methods to get posterior summaries for the change-point of the hazard function considering the exponentiated Weibull distribution.
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| first_indexed | 2024-04-14T03:09:40Z |
| format | Article |
| id | doaj.art-a5aac471085c4420a6e5724d9f3a1718 |
| institution | Directory Open Access Journal |
| issn | 1645-6726 2183-0371 |
| language | English |
| last_indexed | 2024-04-14T03:09:40Z |
| publishDate | 2012-11-01 |
| publisher | Instituto Nacional de Estatística | Statistics Portugal |
| record_format | Article |
| series | Revstat Statistical Journal |
| spelling | doaj.art-a5aac471085c4420a6e5724d9f3a17182022-12-22T02:15:38ZengInstituto Nacional de Estatística | Statistics PortugalRevstat Statistical Journal1645-67262183-03712012-11-0110310.57805/revstat.v10i3.121Inferences for the Change-Point of The Exponentiated Weibull Hazard FunctionJosmar Mazucheli 0Emílio Augusto Coelho-Barros Universidade Estadual de Maringá In many applications of lifetime data analysis, it is important to perform inferences about the change-point of the hazard function. The change-point could be a maximum for unimodal hazard functions or a minimum for bathtub forms of hazard functions and is usually of great interest in medical or industrial applications. For lifetime distributions where this change-point of the hazard function can be analytically calculated, its maximum likelihood estimator is easily obtained from the invariance properties of the maximum likelihood estimators. From the asymptotical normality of the maximum likelihood estimators, confidence intervals can also be obtained. Considering the exponentiated Weibull distribution for the lifetime data, we have different forms for the hazard function: constant, increasing, unimodal, decreasing or bathtub forms. This model gives great flexibility of fit, but we do not have analytic expressions for the change-point of the hazard function. In this way, we consider the use of Markov Chain Monte Carlo methods to get posterior summaries for the change-point of the hazard function considering the exponentiated Weibull distribution. https://revstat.ine.pt/index.php/REVSTAT/article/view/121change-pointexponentiated Weibull distributionhazard functionlifetime data analysisMarkov Chain Monte Carlo |
| spellingShingle | Josmar Mazucheli Emílio Augusto Coelho-Barros Inferences for the Change-Point of The Exponentiated Weibull Hazard Function Revstat Statistical Journal change-point exponentiated Weibull distribution hazard function lifetime data analysis Markov Chain Monte Carlo |
| title | Inferences for the Change-Point of The Exponentiated Weibull Hazard Function |
| title_full | Inferences for the Change-Point of The Exponentiated Weibull Hazard Function |
| title_fullStr | Inferences for the Change-Point of The Exponentiated Weibull Hazard Function |
| title_full_unstemmed | Inferences for the Change-Point of The Exponentiated Weibull Hazard Function |
| title_short | Inferences for the Change-Point of The Exponentiated Weibull Hazard Function |
| title_sort | inferences for the change point of the exponentiated weibull hazard function |
| topic | change-point exponentiated Weibull distribution hazard function lifetime data analysis Markov Chain Monte Carlo |
| url | https://revstat.ine.pt/index.php/REVSTAT/article/view/121 |
| work_keys_str_mv | AT josmarmazucheli inferencesforthechangepointoftheexponentiatedweibullhazardfunction AT emilioaugustocoelhobarros inferencesforthechangepointoftheexponentiatedweibullhazardfunction |