Modeling of Extreme Values via Exponential Normalization Compared with Linear and Power Normalization
Several new asymmetric distributions have arisen naturally in the modeling extreme values are uncovered and elucidated. The present paper deals with the extreme value theorem (EVT) under exponential normalization. An estimate of the shape parameter of the asymmetric generalized value distributions t...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-11-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/12/11/1876 |
| _version_ | 1797547924804075520 |
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| author | Haroon Mohamed Barakat Osama Mohareb Khaled Nourhan Khalil Rakha |
| author_facet | Haroon Mohamed Barakat Osama Mohareb Khaled Nourhan Khalil Rakha |
| author_sort | Haroon Mohamed Barakat |
| collection | DOAJ |
| description | Several new asymmetric distributions have arisen naturally in the modeling extreme values are uncovered and elucidated. The present paper deals with the extreme value theorem (EVT) under exponential normalization. An estimate of the shape parameter of the asymmetric generalized value distributions that related to this new extension of the EVT is obtained. Moreover, we develop the mathematical modeling of the extreme values by using this new extension of the EVT. We analyze the extreme values by modeling the occurrence of the exceedances over high thresholds. The natural distributions of such exceedances, new four generalized Pareto families of asymmetric distributions under exponential normalization (GPDEs), are described and their properties revealed. There is an evident symmetry between the new obtained GPDEs and those generalized Pareto distributions arisen from EVT under linear and power normalization. Estimates for the extreme value index of the four GPDEs are obtained. In addition, simulation studies are conducted in order to illustrate and validate the theoretical results. Finally, a comparison study between the different extreme models is done throughout real data sets. |
| first_indexed | 2024-03-10T14:51:02Z |
| format | Article |
| id | doaj.art-a40e6dd85a764d96b6997b796069d27c |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T14:51:02Z |
| publishDate | 2020-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-a40e6dd85a764d96b6997b796069d27c2023-11-20T20:59:04ZengMDPI AGSymmetry2073-89942020-11-011211187610.3390/sym12111876Modeling of Extreme Values via Exponential Normalization Compared with Linear and Power NormalizationHaroon Mohamed Barakat0Osama Mohareb Khaled1Nourhan Khalil Rakha2Department of Mathematics, Faculty of Science, Zagazig University, 44519 Zagazig, EgyptDepartment of Mathematics, Faculty of Science, Port said University, 42524 Port Said, EgyptDepartment of Physics and Engineering Mathematics, Faculty of Engineering, Port Said University, 42524 Port Said, EgyptSeveral new asymmetric distributions have arisen naturally in the modeling extreme values are uncovered and elucidated. The present paper deals with the extreme value theorem (EVT) under exponential normalization. An estimate of the shape parameter of the asymmetric generalized value distributions that related to this new extension of the EVT is obtained. Moreover, we develop the mathematical modeling of the extreme values by using this new extension of the EVT. We analyze the extreme values by modeling the occurrence of the exceedances over high thresholds. The natural distributions of such exceedances, new four generalized Pareto families of asymmetric distributions under exponential normalization (GPDEs), are described and their properties revealed. There is an evident symmetry between the new obtained GPDEs and those generalized Pareto distributions arisen from EVT under linear and power normalization. Estimates for the extreme value index of the four GPDEs are obtained. In addition, simulation studies are conducted in order to illustrate and validate the theoretical results. Finally, a comparison study between the different extreme models is done throughout real data sets.https://www.mdpi.com/2073-8994/12/11/1876extreme value theorygeneralized extreme value distributiongeneralized Pareto distributionslinear normalizationpower normalizationexponential normalization |
| spellingShingle | Haroon Mohamed Barakat Osama Mohareb Khaled Nourhan Khalil Rakha Modeling of Extreme Values via Exponential Normalization Compared with Linear and Power Normalization Symmetry extreme value theory generalized extreme value distribution generalized Pareto distributions linear normalization power normalization exponential normalization |
| title | Modeling of Extreme Values via Exponential Normalization Compared with Linear and Power Normalization |
| title_full | Modeling of Extreme Values via Exponential Normalization Compared with Linear and Power Normalization |
| title_fullStr | Modeling of Extreme Values via Exponential Normalization Compared with Linear and Power Normalization |
| title_full_unstemmed | Modeling of Extreme Values via Exponential Normalization Compared with Linear and Power Normalization |
| title_short | Modeling of Extreme Values via Exponential Normalization Compared with Linear and Power Normalization |
| title_sort | modeling of extreme values via exponential normalization compared with linear and power normalization |
| topic | extreme value theory generalized extreme value distribution generalized Pareto distributions linear normalization power normalization exponential normalization |
| url | https://www.mdpi.com/2073-8994/12/11/1876 |
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