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A New Reciprocal Weibull Extension for Modeling Extreme Values with Risk Analysis under Insurance Data

Author

Listed:
  • Haitham M. Yousof

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

  • 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)

Abstract

Probability-based distributions might be able to explain risk exposure well. Usually, one number, or at the very least, a limited number of numbers called the key risk indicators (KRIs), are used to describe the level of risk exposure. These risk exposure values, which are undeniably the outcome of a specific model, are frequently referred to as essential critical risk indicators. Five key risk indicators, including value-at-risk, tail variance, tail-value-at-risk, and tail mean-variance, were also used for describing the risk exposure under the reinsurance revenues data. These measurements were created for the proposed model; hence, this paper presents a novel distribution for this purpose. Relevant statistical properties are derived, including the generating function, ordinary moments, and incomplete moments. Special attention is devoted to the applicability of the new model under extreme data sets. Three applications to real data show the usefulness and adaptability of the proposed model. The new model proved its superiority against many well-known related models. Five key risk indicators are employed for analyzing the risk level under the reinsurance revenues dataset. An application is provided along with its relevant numerical analysis and panels. Some useful results are identified and highlighted.

Suggested Citation

  • Haitham M. Yousof & Yusra Tashkandy & Walid Emam & M. Masoom Ali & Mohamed Ibrahim, 2023. "A New Reciprocal Weibull Extension for Modeling Extreme Values with Risk Analysis under Insurance Data," Mathematics, MDPI, vol. 11(4), pages 1-26, February.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:4:p:966-:d:1067453
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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.
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    5. 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.
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    7. 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.
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    Cited by:

    1. Haitham M. Yousof & Hafida Goual & Walid Emam & Yusra Tashkandy & Morad Alizadeh & M. Masoom Ali & Mohamed Ibrahim, 2023. "An Alternative Model for Describing the Reliability Data: Applications, Assessment, and Goodness-of-Fit Validation Testing," Mathematics, MDPI, vol. 11(6), pages 1-26, March.

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