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A flexible extended generalized Pareto distribution for tail estimation

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  • Philémon Gamet
  • Jonathan Jalbert

Abstract

For both financial and environmental applications, tail distributions often correspond to extreme risks and an accurate modeling is mandatory. The peaks‐over‐threshold model is a classic way to model the exceedances over a high threshold with the generalized Pareto distribution. However, for some applications, the choice of a high threshold is challenging and the asymptotic conditions for using this model are not always satisfied. The class of extended generalized Pareto models can be used in this case. However, the existing extended model have either infinite or null density at the threshold, which is not consistent with tail modeling. In the present article, we propose new extensions of the generalized Pareto distribution for which the density at the threshold is positive and finite. The proposed extensions provide better estimate of the upper tail index for low thresholds than existing models. They are also appropriate for high thresholds because in that case, the extended models simplify to the generalize Pareto model. The performance and flexibility of the models are illustrated with the modeling of temperature exceeding a low threshold and non‐zero precipitations recorded in Montreal. For non‐zero precipitation, the very low threshold of 0 is used.

Suggested Citation

  • Philémon Gamet & Jonathan Jalbert, 2022. "A flexible extended generalized Pareto distribution for tail estimation," Environmetrics, John Wiley & Sons, Ltd., vol. 33(6), September.
    • Handle: RePEc:wly:envmet:v:33:y:2022:i:6:n:e2744
    DOI: 10.1002/env.2744
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    References listed on IDEAS

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    1. P. Tencaliec & A.‐C. Favre & P. Naveau & C. Prieur & G. Nicolet, 2020. "Flexible semiparametric generalized Pareto modeling of the entire range of rainfall amount," Environmetrics, John Wiley & Sons, Ltd., vol. 31(2), March.
    2. Michael L. Stein, 2021. "A parametric model for distributions with flexible behaviour in both tails," Environmetrics, John Wiley & Sons, Ltd., vol. 32(8), December.
    3. M. L. Stein, 2017. "Should annual maximum temperatures follow a generalized extreme value distribution?," Biometrika, Biometrika Trust, vol. 104(1), pages 1-16.
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    5. Michael L. Stein, 2021. "A parametric model for distributions with flexible behavior in both tails," Environmetrics, John Wiley & Sons, Ltd., vol. 32(2), March.
    6. Rishikesh Yadav & Raphaël Huser & Thomas Opitz, 2021. "Spatial hierarchical modeling of threshold exceedances using rate mixtures," Environmetrics, John Wiley & Sons, Ltd., vol. 32(3), May.
    7. MacDonald, A. & Scarrott, C.J. & Lee, D. & Darlow, B. & Reale, M. & Russell, G., 2011. "A flexible extreme value mixture model," Computational Statistics & Data Analysis, Elsevier, vol. 55(6), pages 2137-2157, June.
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    Cited by:

    1. Wilson Gyasi & Kahadawala Cooray, 2024. "New generalized extreme value distribution with applications to extreme temperature data," Environmetrics, John Wiley & Sons, Ltd., vol. 35(3), May.
    2. Sweta Rai & Alexis Hoffman & Soumendra Lahiri & Douglas W. Nychka & Stephan R. Sain & Soutir Bandyopadhyay, 2024. "Fast parameter estimation of generalized extreme value distribution using neural networks," Environmetrics, John Wiley & Sons, Ltd., vol. 35(3), May.

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