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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doaj-85c23e16899e436c9bea0738d0a65ece2021-05-17T00:01:37ZengHindawi LimitedJournal of Mathematics2314-47852021-01-01202110.1155/2021/3058170The Exponential T-X Family of Distributions: Properties and an Application to Insurance DataZubair Ahmad0Eisa Mahmoudi1Morad Alizadeh2Rasool Roozegar3Ahmed Z. Afify4Department of StatisticsDepartment of StatisticsDepartment of StatisticsDepartment of StatisticsDepartment of StatisticsHeavy-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 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Zubair Ahmad Eisa Mahmoudi Morad Alizadeh Rasool Roozegar Ahmed Z. Afify |
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 |
author_facet |
Zubair Ahmad Eisa Mahmoudi Morad Alizadeh Rasool Roozegar Ahmed Z. Afify |
author_sort |
Zubair Ahmad |
title |
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_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_sort |
exponential t-x family of distributions: properties and an application to insurance data |
publisher |
Hindawi Limited |
series |
Journal of Mathematics |
issn |
2314-4785 |
publishDate |
2021-01-01 |
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. |
url |
http://dx.doi.org/10.1155/2021/3058170 |
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