The Exponential T-X Family of Distributions: Properties and an Application to Insurance Data. (5th May 2021)

• Record Type: Journal Article
• Authors: Ahmad, Zubair; Mahmoudi, Eisa; Alizadeh, Morad; Roozegar, Rasool; Afify, Ahmed Z.
• Other Names: Koutras Markos Academic Editor.
• Is Part Of: Journal of mathematics. Volume 2021(2021)
• Publication Date: 2021-05-05
• Subjects: Mathematics -- Periodicals; Mathematics; Periodicals; 510
• DOI: 10.1155/2021/3058170
• Languages: English
• ISSNs: 2314-4629

Abstract

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.