On the q-Generalized Extreme Value Distribution
Asymmetrical models such as the Gumbel, logistic, Weibull and generalized extreme value distributions have been extensively utilized for modeling various random phenomena encountered for instance in the course of certain survival, financial or reliability studies. We hereby introduce q-analogues of...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Instituto Nacional de Estatística | Statistics Portugal
2018-02-01
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| Series: | Revstat Statistical Journal |
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| Online Access: | https://revstat.ine.pt/index.php/REVSTAT/article/view/232 |
| _version_ | 1817998363219460096 |
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| author | Serge B. Provost Abdus Saboor Gauss M. Cordeiro Muhammad Mansoor |
| author_facet | Serge B. Provost Abdus Saboor Gauss M. Cordeiro Muhammad Mansoor |
| author_sort | Serge B. Provost |
| collection | DOAJ |
| description |
Asymmetrical models such as the Gumbel, logistic, Weibull and generalized extreme value distributions have been extensively utilized for modeling various random phenomena encountered for instance in the course of certain survival, financial or reliability studies. We hereby introduce q-analogues of the generalized extreme value and Gumbel distributions, the additional parameter q allowing for increased modeling flexibility. These extended models can yield several types of hazard rate functions, and their supports can be finite, infinite as well as bounded above or below. Closed form representations of some statistical functions of the proposed distributions are provided. It is also shown that they compare favorably to three related distributions in connection with the modeling of a certain hydrological data set. Finally, a simulation study confirms the suitability of the maximum likelihood method for estimating the model parameters.
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| first_indexed | 2024-04-14T02:52:07Z |
| format | Article |
| id | doaj.art-1f81e6a01d8045f2aa55c4bfdd2da9ec |
| institution | Directory Open Access Journal |
| issn | 1645-6726 2183-0371 |
| language | English |
| last_indexed | 2024-04-14T02:52:07Z |
| publishDate | 2018-02-01 |
| publisher | Instituto Nacional de Estatística | Statistics Portugal |
| record_format | Article |
| series | Revstat Statistical Journal |
| spelling | doaj.art-1f81e6a01d8045f2aa55c4bfdd2da9ec2022-12-22T02:16:14ZengInstituto Nacional de Estatística | Statistics PortugalRevstat Statistical Journal1645-67262183-03712018-02-0116110.57805/revstat.v16i1.232On the q-Generalized Extreme Value DistributionSerge B. Provost 0Abdus Saboor 1Gauss M. Cordeiro 2Muhammad Mansoor 3The University of Western OntarioKohat University of Science & TechnologyUniversidade Federal de PernambucoThe Islamia University of Bahawalpur Asymmetrical models such as the Gumbel, logistic, Weibull and generalized extreme value distributions have been extensively utilized for modeling various random phenomena encountered for instance in the course of certain survival, financial or reliability studies. We hereby introduce q-analogues of the generalized extreme value and Gumbel distributions, the additional parameter q allowing for increased modeling flexibility. These extended models can yield several types of hazard rate functions, and their supports can be finite, infinite as well as bounded above or below. Closed form representations of some statistical functions of the proposed distributions are provided. It is also shown that they compare favorably to three related distributions in connection with the modeling of a certain hydrological data set. Finally, a simulation study confirms the suitability of the maximum likelihood method for estimating the model parameters. https://revstat.ine.pt/index.php/REVSTAT/article/view/232extreme value theorygeneralized extreme value distributiongoodness-of-fit statisticsGumbel distributionmomentsMonte Carlo simulations |
| spellingShingle | Serge B. Provost Abdus Saboor Gauss M. Cordeiro Muhammad Mansoor On the q-Generalized Extreme Value Distribution Revstat Statistical Journal extreme value theory generalized extreme value distribution goodness-of-fit statistics Gumbel distribution moments Monte Carlo simulations |
| title | On the q-Generalized Extreme Value Distribution |
| title_full | On the q-Generalized Extreme Value Distribution |
| title_fullStr | On the q-Generalized Extreme Value Distribution |
| title_full_unstemmed | On the q-Generalized Extreme Value Distribution |
| title_short | On the q-Generalized Extreme Value Distribution |
| title_sort | on the q generalized extreme value distribution |
| topic | extreme value theory generalized extreme value distribution goodness-of-fit statistics Gumbel distribution moments Monte Carlo simulations |
| url | https://revstat.ine.pt/index.php/REVSTAT/article/view/232 |
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