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Flexible semiparametric generalized Pareto modeling of the entire range of rainfall amount

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  • P. Tencaliec
  • A.‐C. Favre
  • P. Naveau
  • C. Prieur
  • G. Nicolet

Abstract

Precipitation amounts at daily or hourly scales are skewed to the right, and heavy rainfall is poorly modeled by a simple gamma distribution. An important yet challenging topic in hydrometeorology is to find a probability distribution that is able to model well low, moderate, and heavy rainfall. To address this issue, we present a semiparametric distribution suitable for modeling the entire range of rainfall amount. This model is based on a recent parametric statistical model called the class of extended generalized Pareto distributions (EGPDs). The EGPD family is in compliance with extreme value theory for both small and large values, while it keeps a smooth transition between these tails and bypasses the hurdle of selecting thresholds to define extremes. In particular, return levels beyond the largest observation can be inferred. To add flexibility to this EGPD class, we propose to model the transition function in a nonparametric fashion. A fast and efficient nonparametric scheme based on Bernstein polynomial approximations is investigated. We perform simulation studies to assess the performance of our approach. It is compared to two parametric models: a parametric EGPD and the classical generalized Pareto distribution (GPD), the latter being only fitted to excesses above a high threshold. We also apply our semiparametric version of EGPD to a large network of 180 precipitation time series over France.

Suggested Citation

  • 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.
  • Handle: RePEc:wly:envmet:v:31:y:2020:i:2:n:e2582
    DOI: 10.1002/env.2582
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    Cited by:

    1. André, L.M. & Wadsworth, J.L. & O'Hagan, A., 2024. "Joint modelling of the body and tail of bivariate data," Computational Statistics & Data Analysis, Elsevier, vol. 189(C).
    2. Philémon Gamet & Jonathan Jalbert, 2022. "A flexible extended generalized Pareto distribution for tail estimation," Environmetrics, John Wiley & Sons, Ltd., vol. 33(6), September.
    3. Chunli Huang & Xu Zhao & Weihu Cheng & Qingqing Ji & Qiao Duan & Yufei Han, 2022. "Statistical Inference of Dynamic Conditional Generalized Pareto Distribution with Weather and Air Quality Factors," Mathematics, MDPI, vol. 10(9), pages 1-25, April.
    4. Kangyi Li & Yang Zhou, 2024. "Improved Financial Predicting Method Based on Time Series Long Short-Term Memory Algorithm," Mathematics, MDPI, vol. 12(7), pages 1-17, April.
    5. Xiaoting Li & Christian Genest & Jonathan Jalbert, 2021. "A self‐exciting marked point process model for drought analysis," Environmetrics, John Wiley & Sons, Ltd., vol. 32(8), December.
    6. Dacorogna, Michel & Debbabi, Nehla & Kratz, Marie, 2023. "Building up cyber resilience by better grasping cyber risk via a new algorithm for modelling heavy-tailed data," European Journal of Operational Research, Elsevier, vol. 311(2), pages 708-729.
    7. Julie Bessac & Robert Underwood & Sheng Di, 2023. "Discussion on “Saving Storage in Climate Ensembles: A Model-Based Stochastic Approach”," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 28(2), pages 358-364, June.
    8. Gloria Buriticá & Philippe Naveau, 2023. "Stable sums to infer high return levels of multivariate rainfall time series," Environmetrics, John Wiley & Sons, Ltd., vol. 34(4), June.

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