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Probability Models and Statistical Tests for Extreme Precipitation Based on Generalized Negative Binomial Distributions

Author

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  • Victor Korolev

    (Moscow Center for Fundamental and Applied Mathematics, Lomonosov Moscow State University, 119991 Moscow, Russia
    Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, 119991 Moscow, Russia
    Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, 119333 Moscow, Russia
    Department of Mathematics, School of Science, Hangzhou Dianzi University, Hangzhou 310018, China)

  • Andrey Gorshenin

    (Moscow Center for Fundamental and Applied Mathematics, Lomonosov Moscow State University, 119991 Moscow, Russia
    Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, 119991 Moscow, Russia
    Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, 119333 Moscow, Russia)

Abstract

Mathematical models are proposed for statistical regularities of maximum daily precipitation within a wet period and total precipitation volume per wet period. The proposed models are based on the generalized negative binomial (GNB) distribution of the duration of a wet period. The GNB distribution is a mixed Poisson distribution, the mixing distribution being generalized gamma (GG). The GNB distribution demonstrates excellent fit with real data of durations of wet periods measured in days. By means of limit theorems for statistics constructed from samples with random sizes having the GNB distribution, asymptotic approximations are proposed for the distributions of maximum daily precipitation volume within a wet period and total precipitation volume for a wet period. It is shown that the exponent power parameter in the mixing GG distribution matches slow global climate trends. The bounds for the accuracy of the proposed approximations are presented. Several tests for daily precipitation, total precipitation volume and precipitation intensities to be abnormally extremal are proposed and compared to the traditional PoT-method. The results of the application of this test to real data are presented.

Suggested Citation

  • Victor Korolev & Andrey Gorshenin, 2020. "Probability Models and Statistical Tests for Extreme Precipitation Based on Generalized Negative Binomial Distributions," Mathematics, MDPI, vol. 8(4), pages 1-30, April.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:4:p:604-:d:346163
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    References listed on IDEAS

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    1. Whitney K. Huang & Douglas W. Nychka & Hao Zhang, 2019. "Estimating precipitation extremes using the log‐histospline," Environmetrics, John Wiley & Sons, Ltd., vol. 30(4), June.
    2. Victor Korolev & Andrey Gorshenin & Konstatin Belyaev, 2019. "Statistical Tests for Extreme Precipitation Volumes," Mathematics, MDPI, vol. 7(7), pages 1-20, July.
    3. Korolev, V.Yu. & Chertok, A.V. & Korchagin, A.Yu. & Zeifman, A.I., 2015. "Modeling high-frequency order flow imbalance by functional limit theorems for two-sided risk processes," Applied Mathematics and Computation, Elsevier, vol. 253(C), pages 224-241.
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    Cited by:

    1. Gerd Christoph & Vladimir V. Ulyanov, 2023. "Second Order Chebyshev–Edgeworth-Type Approximations for Statistics Based on Random Size Samples," Mathematics, MDPI, vol. 11(8), pages 1-18, April.
    2. Victor Korolev, 2022. "Bounds for the Rate of Convergence in the Generalized Rényi Theorem," Mathematics, MDPI, vol. 10(22), pages 1-16, November.
    3. Andrey Gorshenin & Victor Kuzmin, 2022. "Statistical Feature Construction for Forecasting Accuracy Increase and Its Applications in Neural Network Based Analysis," Mathematics, MDPI, vol. 10(4), pages 1-21, February.

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