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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Bibliographic Details
Published in:Journal of mathematics (Hidawi) 2021, Vol.2021, p.1-18
Main Authors: Ahmad, Zubair, Mahmoudi, Eisa, Alizadeh, Morad, Roozegar, Rasool, Afify, Ahmed Z.
Format: Article
Language:English
Subjects:
Automobile insurance
Insurance
Mathematics
Maximum likelihood estimates
Maximum likelihood estimators
Methods
Monte Carlo simulation
Parameter estimation
Probability
Random variables
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Summary: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.
ISSN:2314-4629
2314-4785
DOI:10.1155/2021/3058170