On the Asymptotic Behavior of the Maximum and Record Values of Multivariate Data Using the R-ordering principle
By using a sup-norm, sufficient conditions for the convergence of multivariate extremes and the potential limit types were fully identified by Barakat et al. (2020a). In this paper, we prove an intriguing result that by using the sup-norm, the weak convergence of multivariate extremes to the Fréchet...
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University of Bologna
2024-12-01
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| Series: | Statistica |
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| Online Access: | https://rivista-statistica.unibo.it/article/view/17805 |
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| author | Mahmoud H. Harpy Haroon M. Barakat |
| author_facet | Mahmoud H. Harpy Haroon M. Barakat |
| author_sort | Mahmoud H. Harpy |
| collection | DOAJ |
| description | By using a sup-norm, sufficient conditions for the convergence of multivariate extremes and the potential limit types were fully identified by Barakat et al. (2020a). In this paper, we prove an intriguing result that by using the sup-norm, the weak convergence of multivariate extremes to the Fréchet type implies the convergence of those multivariate extremes in an arbitrary D-normto the same type-limit by using the same normalizing constants. As a result of this finding, the weak convergence to the Fréchet type takes place by employing any logistic norm. Moreover, the two other possible limit types (max-Weibull and Gumbel types) are discussed. Similar findings are also demonstrated for multivariate record values. Finally, we demonstrate in a real-world scenario how to model multivariate extreme data sets utilizing the R-ordering principle and different norms. |
| format | Article |
| id | doaj-art-9cacc7593f7246e1a2f96b0d8ecc7a2b |
| institution | Kabale University |
| issn | 0390-590X 1973-2201 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | University of Bologna |
| record_format | Article |
| series | Statistica |
| spelling | doaj-art-9cacc7593f7246e1a2f96b0d8ecc7a2b2025-01-09T08:39:05ZengUniversity of BolognaStatistica0390-590X1973-22012024-12-0183216517910.6092/issn.1973-2201/1780516164On the Asymptotic Behavior of the Maximum and Record Values of Multivariate Data Using the R-ordering principleMahmoud H. Harpy0Haroon M. Barakat1Prince Sattam Bin Abdulaziz University, Saudi ArabiaZagazig University, EgyptBy using a sup-norm, sufficient conditions for the convergence of multivariate extremes and the potential limit types were fully identified by Barakat et al. (2020a). In this paper, we prove an intriguing result that by using the sup-norm, the weak convergence of multivariate extremes to the Fréchet type implies the convergence of those multivariate extremes in an arbitrary D-normto the same type-limit by using the same normalizing constants. As a result of this finding, the weak convergence to the Fréchet type takes place by employing any logistic norm. Moreover, the two other possible limit types (max-Weibull and Gumbel types) are discussed. Similar findings are also demonstrated for multivariate record values. Finally, we demonstrate in a real-world scenario how to model multivariate extreme data sets utilizing the R-ordering principle and different norms.https://rivista-statistica.unibo.it/article/view/17805weak convergence multivariate extremesreduced ordering principlesup-norm logistic-normd-norm |
| spellingShingle | Mahmoud H. Harpy Haroon M. Barakat On the Asymptotic Behavior of the Maximum and Record Values of Multivariate Data Using the R-ordering principle Statistica weak convergence multivariate extremes reduced ordering principle sup-norm logistic-norm d-norm |
| title | On the Asymptotic Behavior of the Maximum and Record Values of Multivariate Data Using the R-ordering principle |
| title_full | On the Asymptotic Behavior of the Maximum and Record Values of Multivariate Data Using the R-ordering principle |
| title_fullStr | On the Asymptotic Behavior of the Maximum and Record Values of Multivariate Data Using the R-ordering principle |
| title_full_unstemmed | On the Asymptotic Behavior of the Maximum and Record Values of Multivariate Data Using the R-ordering principle |
| title_short | On the Asymptotic Behavior of the Maximum and Record Values of Multivariate Data Using the R-ordering principle |
| title_sort | on the asymptotic behavior of the maximum and record values of multivariate data using the r ordering principle |
| topic | weak convergence multivariate extremes reduced ordering principle sup-norm logistic-norm d-norm |
| url | https://rivista-statistica.unibo.it/article/view/17805 |
| work_keys_str_mv | AT mahmoudhharpy ontheasymptoticbehaviorofthemaximumandrecordvaluesofmultivariatedatausingtherorderingprinciple AT haroonmbarakat ontheasymptoticbehaviorofthemaximumandrecordvaluesofmultivariatedatausingtherorderingprinciple |