The Exponential T-X Family of Distributions: Properties and an Application to Insurance Data

Zubair Ahmad, Eisa Mahmoudi, Morad Alizadeh, Rasool Roozegar, Ahmed Z. Afify and Markos Koutras

Journal of Mathematics, 2021, vol. 2021, 1-18

Abstract: 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.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:3058170

DOI: 10.1155/2021/3058170

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