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A Novel Model for Quantitative Risk Assessment under Claim-Size Data with Bimodal and Symmetric Data Modeling

Author

Listed:
  • Haitham M. Yousof

    (Department of Statistics, Mathematics and Insurance, Benha University, Benha 13518, Egypt)

  • Walid Emam

    (Department of Statistics and Operations Research, Faculty of Science, King Saud University, Riyadh 11451, Saudi Arabia)

  • Yusra Tashkandy

    (Department of Statistics and Operations Research, Faculty of Science, King Saud University, Riyadh 11451, Saudi Arabia)

  • M. Masoom Ali

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

  • R. Minkah

    (Department of Statistics and Actuarial Science, School of Physical and Mathematical Science, College of Basic and Applied Science, Accra 00233, Ghana)

  • Mohamed Ibrahim

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

Abstract

A novel flexible extension of the Chen distribution is defined and studied in this paper. Relevant statistical properties of the novel model are derived. For the actuarial risk analysis and evaluation, the maximum likelihood, weighted least squares, ordinary least squares, Cramer–von Mises, moments, and Anderson–Darling methods are utilized. For actuarial purposes, a comprehensive simulation study is presented using various combinations to evaluate the performance of the six methods in analyzing insurance risks. These six methods are used in evaluating actuarial risks using insurance claims data. Two applications on bimodal data are presented to highlight the flexibility and relevance of the new distribution. The new distribution is compared to several competing distributions. Actuarial risks are analyzed and evaluated using actuarial data, and the ability to disclose actuarial risks is compared by a comprehensive simulation study, through which actuarial disclosure models are compared using a wide range of well-known models.

Suggested Citation

  • Haitham M. Yousof & Walid Emam & Yusra Tashkandy & M. Masoom Ali & R. Minkah & Mohamed Ibrahim, 2023. "A Novel Model for Quantitative Risk Assessment under Claim-Size Data with Bimodal and Symmetric Data Modeling," Mathematics, MDPI, vol. 11(6), pages 1-31, March.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:6:p:1284-:d:1090308
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    References listed on IDEAS

    as
    1. Julia Lynn Wirch, 1999. "Raising Value at Risk," North American Actuarial Journal, Taylor & Francis Journals, vol. 3(2), pages 106-115.
    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.
    3. Landsman, Zinoviy, 2010. "On the Tail Mean-Variance optimal portfolio selection," Insurance: Mathematics and Economics, Elsevier, vol. 46(3), pages 547-553, June.
    4. Acerbi, Carlo & Tasche, Dirk, 2002. "On the coherence of expected shortfall," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1487-1503, July.
    5. Chen, Zhenmin, 2000. "A new two-parameter lifetime distribution with bathtub shape or increasing failure rate function," Statistics & Probability Letters, Elsevier, vol. 49(2), pages 155-161, August.
    6. 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.
    7. Furman, Edward & Landsman, Zinoviy, 2006. "Tail Variance Premium with Applications for Elliptical Portfolio of Risks," ASTIN Bulletin, Cambridge University Press, vol. 36(2), pages 433-462, November.
    Full references (including those not matched with items on IDEAS)

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