A Novel Model for Quantitative Risk Assessment under Claim-Size Data with Bimodal and Symmetric Data Modeling
A novel flexible extension of the Chen distribution is defined and studied in this paper. Relevant statistical properties of the novel model are derived. For the actuarial risk analysis and evaluation, the maximum likelihood, weighted least squares, ordinary least squares, Cramer–von Mises, moments,...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-03-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/6/1284 |
| _version_ | 1797610359500046336 |
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| author | Haitham M. Yousof Walid Emam Yusra Tashkandy M. Masoom Ali R. Minkah Mohamed Ibrahim |
| author_facet | Haitham M. Yousof Walid Emam Yusra Tashkandy M. Masoom Ali R. Minkah Mohamed Ibrahim |
| author_sort | Haitham M. Yousof |
| collection | DOAJ |
| description | A novel flexible extension of the Chen distribution is defined and studied in this paper. Relevant statistical properties of the novel model are derived. For the actuarial risk analysis and evaluation, the maximum likelihood, weighted least squares, ordinary least squares, Cramer–von Mises, moments, and Anderson–Darling methods are utilized. For actuarial purposes, a comprehensive simulation study is presented using various combinations to evaluate the performance of the six methods in analyzing insurance risks. These six methods are used in evaluating actuarial risks using insurance claims data. Two applications on bimodal data are presented to highlight the flexibility and relevance of the new distribution. The new distribution is compared to several competing distributions. Actuarial risks are analyzed and evaluated using actuarial data, and the ability to disclose actuarial risks is compared by a comprehensive simulation study, through which actuarial disclosure models are compared using a wide range of well-known models. |
| first_indexed | 2024-03-11T06:13:19Z |
| format | Article |
| id | doaj.art-5d434f068c1145b9a97fb16d47a052cd |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T06:13:19Z |
| publishDate | 2023-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-5d434f068c1145b9a97fb16d47a052cd2023-11-17T12:26:27ZengMDPI AGMathematics2227-73902023-03-01116128410.3390/math11061284A Novel Model for Quantitative Risk Assessment under Claim-Size Data with Bimodal and Symmetric Data ModelingHaitham M. Yousof0Walid Emam1Yusra Tashkandy2M. Masoom Ali3R. Minkah4Mohamed Ibrahim5Department of Statistics, Mathematics and Insurance, Benha University, Benha 13518, EgyptDepartment of Statistics and Operations Research, Faculty of Science, King Saud University, Riyadh 11451, Saudi ArabiaDepartment of Statistics and Operations Research, Faculty of Science, King Saud University, Riyadh 11451, Saudi ArabiaDepartment of Mathematical Sciences, Ball State University, Muncie, IN 47306, USADepartment of Statistics and Actuarial Science, School of Physical and Mathematical Science, College of Basic and Applied Science, Accra 00233, GhanaDepartment of Applied, Mathematical and Actuarial Statistics, Faculty of Commerce, Damietta University, Damietta 34517, EgyptA novel flexible extension of the Chen distribution is defined and studied in this paper. Relevant statistical properties of the novel model are derived. For the actuarial risk analysis and evaluation, the maximum likelihood, weighted least squares, ordinary least squares, Cramer–von Mises, moments, and Anderson–Darling methods are utilized. For actuarial purposes, a comprehensive simulation study is presented using various combinations to evaluate the performance of the six methods in analyzing insurance risks. These six methods are used in evaluating actuarial risks using insurance claims data. Two applications on bimodal data are presented to highlight the flexibility and relevance of the new distribution. The new distribution is compared to several competing distributions. Actuarial risks are analyzed and evaluated using actuarial data, and the ability to disclose actuarial risks is compared by a comprehensive simulation study, through which actuarial disclosure models are compared using a wide range of well-known models.https://www.mdpi.com/2227-7390/11/6/1284actuarial risksasymmetric data setleft skewed claimslikelihoodbimodal datavalue-at-risk |
| spellingShingle | Haitham M. Yousof Walid Emam Yusra Tashkandy M. Masoom Ali R. Minkah Mohamed Ibrahim A Novel Model for Quantitative Risk Assessment under Claim-Size Data with Bimodal and Symmetric Data Modeling Mathematics actuarial risks asymmetric data set left skewed claims likelihood bimodal data value-at-risk |
| title | A Novel Model for Quantitative Risk Assessment under Claim-Size Data with Bimodal and Symmetric Data Modeling |
| title_full | A Novel Model for Quantitative Risk Assessment under Claim-Size Data with Bimodal and Symmetric Data Modeling |
| title_fullStr | A Novel Model for Quantitative Risk Assessment under Claim-Size Data with Bimodal and Symmetric Data Modeling |
| title_full_unstemmed | A Novel Model for Quantitative Risk Assessment under Claim-Size Data with Bimodal and Symmetric Data Modeling |
| title_short | A Novel Model for Quantitative Risk Assessment under Claim-Size Data with Bimodal and Symmetric Data Modeling |
| title_sort | novel model for quantitative risk assessment under claim size data with bimodal and symmetric data modeling |
| topic | actuarial risks asymmetric data set left skewed claims likelihood bimodal data value-at-risk |
| url | https://www.mdpi.com/2227-7390/11/6/1284 |
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