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

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

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.

Suggested Citation

  • Zubair Ahmad & Eisa Mahmoudi & Morad Alizadeh & Rasool Roozegar & Ahmed Z. Afify & Markos Koutras, 2021. "The Exponential T-X Family of Distributions: Properties and an Application to Insurance Data," Journal of Mathematics, Hindawi, vol. 2021, pages 1-18, May.
    • Handle: RePEc:hin:jjmath:3058170
    DOI: 10.1155/2021/3058170
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    Cited by:

    1. Zubair Ahmad & Zahra Almaspoor & Faridoon Khan & Mahmoud El-Morshedy, 2022. "On Predictive Modeling Using a New Flexible Weibull Distribution and Machine Learning Approach: Analyzing the COVID-19 Data," Mathematics, MDPI, vol. 10(11), pages 1-26, May.
    2. Broderick Oluyede & Thatayaone Moakofi, 2023. "The Gamma-Topp-Leone-Type II-Exponentiated Half Logistic-G Family of Distributions with Applications," Stats, MDPI, vol. 6(2), pages 1-28, June.

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