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Risk Analysis and Estimation of a Bimodal Heavy-Tailed Burr XII Model in Insurance Data: Exploring Multiple Methods and Applications

Author

Listed:
  • Haitham M. Yousof

    (Department of Statistics, Mathematics and Insurance, Benha University, Benha 13511, Egypt)

  • S. I. Ansari

    (Department of Business Administration, Azad Institute of Engineering and Technology, Lucknow 226002, India)

  • Yusra Tashkandy

    (Department of Statistics and Operations Research, Faculty of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia)

  • Walid Emam

    (Department of Statistics and Operations Research, Faculty of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia)

  • M. Masoom Ali

    (Department of Mathematical Sciences, Ball State University, Muncie, IN 47306, USA)

  • Mohamed Ibrahim

    (Department of Applied, Mathematical and Actuarial Statistics, Faculty of Commerce, Damietta University, Damietta 34517, Egypt)

  • Salwa L. Alkhayyat

    (Department of Statistics, Mathematics and Insurance, Faculty of Commerce, Kafr El-Sheikh University, Kafr El-Sheikh 33511, Egypt)

Abstract

Actuarial risks can be analyzed using heavy-tailed distributions, which provide adequate risk assessment. Key risk indicators, such as value-at-risk, tailed-value-at-risk (conditional tail expectation), tailed-variance, tailed-mean-variance, and mean excess loss function, are commonly used to evaluate risk exposure levels. In this study, we analyze actuarial risks using these five indicators, calculated using four different estimation methods: maximum likelihood, ordinary least square, weighted least square, and Cramer-Von-Mises. To achieve our main goal, we introduce and study a new distribution. Monte Carlo simulations are used to assess the performance of all estimation methods. We provide two real-life datasets with two applications to compare the classical methods and demonstrate the importance of the proposed model, evaluated via the maximum likelihood method. Finally, we evaluate and analyze actuarial risks using the abovementioned methods and five actuarial indicators based on bimodal insurance claim payments data.

Suggested Citation

  • Haitham M. Yousof & S. I. Ansari & Yusra Tashkandy & Walid Emam & M. Masoom Ali & Mohamed Ibrahim & Salwa L. Alkhayyat, 2023. "Risk Analysis and Estimation of a Bimodal Heavy-Tailed Burr XII Model in Insurance Data: Exploring Multiple Methods and Applications," Mathematics, MDPI, vol. 11(9), pages 1-26, May.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:9:p:2179-:d:1140081
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    References listed on IDEAS

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    1. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    2. Philippe Artzner, 1999. "Application of Coherent Risk Measures to Capital Requirements in Insurance," North American Actuarial Journal, Taylor & Francis Journals, vol. 3(2), pages 11-25.
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