Return Level Prediction with a New Mixture Extreme Value Model

Emrah Altun (), Hana N. Alqifari and Kadir Söyler
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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

Mathematics, 2025, vol. 13, issue 17, 1-24

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.

Keywords: return level; extreme value distribution; exponentiated Pareto; simulation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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