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Abstract
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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.
(e 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. (e
proposed model is compared with some well-known competing distributions.
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