The Exponential T-X Family of Distributions: Properties and an Application to Insurance Data
Heavy-tailed distributions play a prominent role in actuarial and financial sciences. In this paper, we introduce a family of distributions that we refer to as exponential T-X (ETX) family. Based on the proposed approach, a new extension of the Weibull model is introduced. The proposed model is very...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/3058170 |
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| author | Zubair Ahmad Eisa Mahmoudi Morad Alizadeh Rasool Roozegar Ahmed Z. Afify |
| author_facet | Zubair Ahmad Eisa Mahmoudi Morad Alizadeh Rasool Roozegar Ahmed Z. Afify |
| author_sort | Zubair Ahmad |
| collection | DOAJ |
| description | Heavy-tailed distributions play a prominent role in actuarial and financial sciences. In this paper, we introduce a family of distributions that we refer to as exponential T-X (ETX) family. Based on the proposed approach, a new extension of the Weibull model is introduced. The proposed model is very flexible in modeling heavy-tailed data. Some mathematical properties are derived, and maximum likelihood estimates of the model parameters are obtained. A Monte Carlo simulation study is conducted to evaluate the performance of the maximum likelihood estimators. Actuarial measures such as value at risk and tail value at risk are also calculated. A simulation study based on these actuarial measures is provided. Finally, an application to a heavy-tailed automobile insurance claim data set is presented. The proposed model is compared with some well-known competing distributions. |
| format | Article |
| id | doaj-art-85c23e16899e436c9bea0738d0a65ece |
| institution | OA Journals |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-85c23e16899e436c9bea0738d0a65ece2025-08-20T02:08:56ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/30581703058170The Exponential T-X Family of Distributions: Properties and an Application to Insurance DataZubair Ahmad0Eisa Mahmoudi1Morad Alizadeh2Rasool Roozegar3Ahmed Z. Afify4Department of Statistics, Yazd University, P.O. Box 89175-741, Yazd, IranDepartment of Statistics, Yazd University, P.O. Box 89175-741, Yazd, IranDepartment of Statistics, Persian Gulf University, Bushehr 75169, IranDepartment of Statistics, Yazd University, P.O. Box 89175-741, Yazd, IranDepartment of Statistics, Mathematics and Insurance, Benha University, Benha 13511, EgyptHeavy-tailed distributions play a prominent role in actuarial and financial sciences. In this paper, we introduce a family of distributions that we refer to as exponential T-X (ETX) family. Based on the proposed approach, a new extension of the Weibull model is introduced. The proposed model is very flexible in modeling heavy-tailed data. Some mathematical properties are derived, and maximum likelihood estimates of the model parameters are obtained. A Monte Carlo simulation study is conducted to evaluate the performance of the maximum likelihood estimators. Actuarial measures such as value at risk and tail value at risk are also calculated. A simulation study based on these actuarial measures is provided. Finally, an application to a heavy-tailed automobile insurance claim data set is presented. The proposed model is compared with some well-known competing distributions.http://dx.doi.org/10.1155/2021/3058170 |
| spellingShingle | Zubair Ahmad Eisa Mahmoudi Morad Alizadeh Rasool Roozegar Ahmed Z. Afify The Exponential T-X Family of Distributions: Properties and an Application to Insurance Data Journal of Mathematics |
| title | The Exponential T-X Family of Distributions: Properties and an Application to Insurance Data |
| title_full | The Exponential T-X Family of Distributions: Properties and an Application to Insurance Data |
| title_fullStr | The Exponential T-X Family of Distributions: Properties and an Application to Insurance Data |
| title_full_unstemmed | The Exponential T-X Family of Distributions: Properties and an Application to Insurance Data |
| title_short | The Exponential T-X Family of Distributions: Properties and an Application to Insurance Data |
| title_sort | exponential t x family of distributions properties and an application to insurance data |
| url | http://dx.doi.org/10.1155/2021/3058170 |
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