The Arcsine Exponentiated-X Family: Validation and Insurance Application
In this paper, we propose a family of heavy tailed distributions, by incorporating a trigonometric function called the arcsine exponentiated-X family of distributions. Based on the proposed approach, a three-parameter extension of the Weibull distribution called the arcsine exponentiated-Weibull (AS...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2020/8394815 |
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| author | Wenjing He Zubair Ahmad Ahmed Z. Afify Hafida Goual |
| author_facet | Wenjing He Zubair Ahmad Ahmed Z. Afify Hafida Goual |
| author_sort | Wenjing He |
| collection | DOAJ |
| description | In this paper, we propose a family of heavy tailed distributions, by incorporating a trigonometric function called the arcsine exponentiated-X family of distributions. Based on the proposed approach, a three-parameter extension of the Weibull distribution called the arcsine exponentiated-Weibull (ASE-W) distribution is studied in detail. Maximum likelihood is used to estimate the model parameters, and its performance is evaluated by two simulation studies. Actuarial measures including Value at Risk and Tail Value at Risk are derived for the ASE-W distribution. Furthermore, a numerical study of these measures is conducted proving that the proposed ASE-W distribution has a heavier tail than the baseline Weibull distribution. These actuarial measures are also estimated from insurance claims real data for the ASE-W and other competing distributions. The usefulness and flexibility of the proposed model is proved by analyzing a real-life heavy tailed insurance claims data. We construct a modified chi-squared goodness-of-fit test based on the Nikulin–Rao–Robson statistic to verify the validity of the proposed ASE-W model. The modified test shows that the ASE-W model can be used as a good candidate for analyzing heavy tailed insurance claims data. |
| format | Article |
| id | doaj-art-8fc45f8800e34a4188f608724055b484 |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-8fc45f8800e34a4188f608724055b4842025-02-03T01:04:14ZengWileyComplexity1076-27871099-05262020-01-01202010.1155/2020/83948158394815The Arcsine Exponentiated-X Family: Validation and Insurance ApplicationWenjing He0Zubair Ahmad1Ahmed Z. Afify2Hafida Goual3College of Modern Economics and Management, Jiangxi University of Finance and Economics, Nanchang, Jiangxi, ChinaDepartment of Statistics, Yazd University, P.O. Box 89175-741, Yazd, IranDepartment of Statistics, Mathematics and Insurance, Benha University, Benha, EgyptLaboratory of Probability and Statistics University of Badji Mokhtar, Annaba, AlgeriaIn this paper, we propose a family of heavy tailed distributions, by incorporating a trigonometric function called the arcsine exponentiated-X family of distributions. Based on the proposed approach, a three-parameter extension of the Weibull distribution called the arcsine exponentiated-Weibull (ASE-W) distribution is studied in detail. Maximum likelihood is used to estimate the model parameters, and its performance is evaluated by two simulation studies. Actuarial measures including Value at Risk and Tail Value at Risk are derived for the ASE-W distribution. Furthermore, a numerical study of these measures is conducted proving that the proposed ASE-W distribution has a heavier tail than the baseline Weibull distribution. These actuarial measures are also estimated from insurance claims real data for the ASE-W and other competing distributions. The usefulness and flexibility of the proposed model is proved by analyzing a real-life heavy tailed insurance claims data. We construct a modified chi-squared goodness-of-fit test based on the Nikulin–Rao–Robson statistic to verify the validity of the proposed ASE-W model. The modified test shows that the ASE-W model can be used as a good candidate for analyzing heavy tailed insurance claims data.http://dx.doi.org/10.1155/2020/8394815 |
| spellingShingle | Wenjing He Zubair Ahmad Ahmed Z. Afify Hafida Goual The Arcsine Exponentiated-X Family: Validation and Insurance Application Complexity |
| title | The Arcsine Exponentiated-X Family: Validation and Insurance Application |
| title_full | The Arcsine Exponentiated-X Family: Validation and Insurance Application |
| title_fullStr | The Arcsine Exponentiated-X Family: Validation and Insurance Application |
| title_full_unstemmed | The Arcsine Exponentiated-X Family: Validation and Insurance Application |
| title_short | The Arcsine Exponentiated-X Family: Validation and Insurance Application |
| title_sort | arcsine exponentiated x family validation and insurance application |
| url | http://dx.doi.org/10.1155/2020/8394815 |
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