A New Heavy-Tailed Lomax Model With Characterizations, Applications, Peaks Over Random Threshold Value-at-Risk, and the Mean-of-Order-P Analysis
In this work, a new heavy-tailed Lomax model is proposed for the reliability and actuarial risk analysis. Simulations are conducted to investigate how the estimators behave. Parameters are derived through maximum likelihood estimation techniques. The efficacy of the newly proposed heavy-tailed Loma...
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| Main Authors: | , , , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2024-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/jom/5329529 |
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| author | M. I. Khan Abdussalam Aljadani Mahmoud M. Mansour Enayat M. Abd Elrazik G. G. Hamedani Haitham M. Yousof Wahid A. M. Shehata |
| author_facet | M. I. Khan Abdussalam Aljadani Mahmoud M. Mansour Enayat M. Abd Elrazik G. G. Hamedani Haitham M. Yousof Wahid A. M. Shehata |
| author_sort | M. I. Khan |
| collection | DOAJ |
| description | In this work, a new heavy-tailed Lomax model is proposed for the reliability and actuarial risk analysis. Simulations are conducted to investigate how the estimators behave. Parameters are derived through maximum likelihood estimation techniques. The efficacy of the newly proposed heavy-tailed Loma distribution is illustrated using the USA indemnity loss datasets. The findings clearly indicate that the new loss model offers a superior parametric fit compared to other competing distributions. Analyzing metrics such as value-at-risk, tail mean variance, tail variance, peaks over a random threshold value-at-risk (PORT-VAR), and the mean-of-order-P (MOP(P)) can aid in risk assessment and in identifying and describing significant events or outliers within the USA indemnity loss. This research introduces PORT-VAR estimators tailored specifically for risk analysis using the USA indemnity loss dataset. The study emphasizes determining the optimal order of P based on the true mean value to enhance the characterization of critical events in the dataset. |
| format | Article |
| id | doaj-art-6166fc7b9a2240e49cfe6524d1ed9283 |
| institution | OA Journals |
| issn | 2314-4785 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-6166fc7b9a2240e49cfe6524d1ed92832025-08-20T01:56:39ZengWileyJournal of Mathematics2314-47852024-01-01202410.1155/jom/5329529A New Heavy-Tailed Lomax Model With Characterizations, Applications, Peaks Over Random Threshold Value-at-Risk, and the Mean-of-Order-P AnalysisM. I. Khan0Abdussalam Aljadani1Mahmoud M. Mansour2Enayat M. Abd Elrazik3G. G. Hamedani4Haitham M. Yousof5Wahid A. M. Shehata6Department of MathematicsDepartment of ManagementManagement Information Systems DepartmentManagement Information Systems DepartmentDepartment of Mathematical and Statistical SciencesDepartment of StatisticsDepartment of MathematicsIn this work, a new heavy-tailed Lomax model is proposed for the reliability and actuarial risk analysis. Simulations are conducted to investigate how the estimators behave. Parameters are derived through maximum likelihood estimation techniques. The efficacy of the newly proposed heavy-tailed Loma distribution is illustrated using the USA indemnity loss datasets. The findings clearly indicate that the new loss model offers a superior parametric fit compared to other competing distributions. Analyzing metrics such as value-at-risk, tail mean variance, tail variance, peaks over a random threshold value-at-risk (PORT-VAR), and the mean-of-order-P (MOP(P)) can aid in risk assessment and in identifying and describing significant events or outliers within the USA indemnity loss. This research introduces PORT-VAR estimators tailored specifically for risk analysis using the USA indemnity loss dataset. The study emphasizes determining the optimal order of P based on the true mean value to enhance the characterization of critical events in the dataset.http://dx.doi.org/10.1155/jom/5329529 |
| spellingShingle | M. I. Khan Abdussalam Aljadani Mahmoud M. Mansour Enayat M. Abd Elrazik G. G. Hamedani Haitham M. Yousof Wahid A. M. Shehata A New Heavy-Tailed Lomax Model With Characterizations, Applications, Peaks Over Random Threshold Value-at-Risk, and the Mean-of-Order-P Analysis Journal of Mathematics |
| title | A New Heavy-Tailed Lomax Model With Characterizations, Applications, Peaks Over Random Threshold Value-at-Risk, and the Mean-of-Order-P Analysis |
| title_full | A New Heavy-Tailed Lomax Model With Characterizations, Applications, Peaks Over Random Threshold Value-at-Risk, and the Mean-of-Order-P Analysis |
| title_fullStr | A New Heavy-Tailed Lomax Model With Characterizations, Applications, Peaks Over Random Threshold Value-at-Risk, and the Mean-of-Order-P Analysis |
| title_full_unstemmed | A New Heavy-Tailed Lomax Model With Characterizations, Applications, Peaks Over Random Threshold Value-at-Risk, and the Mean-of-Order-P Analysis |
| title_short | A New Heavy-Tailed Lomax Model With Characterizations, Applications, Peaks Over Random Threshold Value-at-Risk, and the Mean-of-Order-P Analysis |
| title_sort | new heavy tailed lomax model with characterizations applications peaks over random threshold value at risk and the mean of order p analysis |
| url | http://dx.doi.org/10.1155/jom/5329529 |
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