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Return Level Prediction with a New Mixture Extreme Value Model

Author

Listed:
  • Emrah Altun

    (Department of Statistics, Gazi University, Ankara 06560, Turkey)

  • Hana N. Alqifari

    (Department of Statistics and Operations Research, College of Science, Qassim University, Buraydah 51482, Saudi Arabia)

  • Kadir Söyler

    (Department of Mathematics, Bartin University, Bartin 74100, Turkey)

Abstract

The generalized Pareto distribution is frequently used for modeling extreme values above an appropriate threshold level. Since the process of determining the appropriate threshold value is difficult, a mixture of extreme value models rises to prominence. In this study, mixture extreme value models based on exponentiated Pareto distribution are proposed. The Weibull, gamma, and log-normal models are used as bulk densities. The parameter estimates of the proposed models are obtained using the maximum likelihood approach. Two different approaches based on maximization of the log-likelihood and Kolmogorov–Smirnov p -value are used to determine the appropriate threshold value. The effectiveness of these methods is compared using simulation studies. The proposed models are compared with other mixture models through an application study on earthquake data. The GammaEP web application is developed to ensure the reproducibility of the results and the usability of the proposed model.

Suggested Citation

  • Emrah Altun & Hana N. Alqifari & Kadir Söyler, 2025. "Return Level Prediction with a New Mixture Extreme Value Model," Mathematics, MDPI, vol. 13(17), pages 1-24, August.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:17:p:2705-:d:1730378
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    References listed on IDEAS

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