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

• Main Authors: Zubair Ahmad, Eisa Mahmoudi, Morad Alizadeh, Rasool Roozegar, Ahmed Z. Afify
• Format: Article
• Language: English
• Published: Hindawi Limited 2021-01-01
• Series: Journal of Mathematics
• Online Access: http://dx.doi.org/10.1155/2021/3058170

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.