IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i4p604-d346163.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/4/604/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/8/4/604/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Victor Korolev, 2022. "Bounds for the Rate of Convergence in the Generalized Rényi Theorem," Mathematics, MDPI, vol. 10(22), pages 1-16, November.
    2. 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.
    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Carlynn Fagnant & Avantika Gori & Antonia Sebastian & Philip B. Bedient & Katherine B. Ensor, 2020. "Characterizing spatiotemporal trends in extreme precipitation in Southeast Texas," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 104(2), pages 1597-1621, November.
    2. Chang Yu & Ondrej Blaha & Michael Kane & Wei Wei & Denise Esserman & Daniel Zelterman, 2022. "Regression methods for the appearances of extremes in climate data," Environmetrics, John Wiley & Sons, Ltd., vol. 33(7), November.
    3. Michael L. Stein, 2021. "A parametric model for distributions with flexible behavior in both tails," Environmetrics, John Wiley & Sons, Ltd., vol. 32(2), March.
    4. Luca Pratelli & Pietro Rigo, 2021. "Convergence in Total Variation of Random Sums," Mathematics, MDPI, vol. 9(2), pages 1-11, January.
    5. Brook T. Russell & Whitney K. Huang, 2021. "Modeling short‐ranged dependence in block extrema with application to polar temperature data," Environmetrics, John Wiley & Sons, Ltd., vol. 32(3), May.
    6. Konark Jain & Nick Firoozye & Jonathan Kochems & Philip Treleaven, 2024. "Limit Order Book Simulations: A Review," Papers 2402.17359, arXiv.org, revised Mar 2024.
    7. 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).
    8. Korolev, Victor & Zeifman, Alexander, 2021. "Bounds for convergence rate in laws of large numbers for mixed Poisson random sums," Statistics & Probability Letters, Elsevier, vol. 168(C).
    9. Victor Korolev & Andrey Gorshenin & Konstatin Belyaev, 2019. "Statistical Tests for Extreme Precipitation Volumes," Mathematics, MDPI, vol. 7(7), pages 1-20, July.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:8:y:2020:i:4:p:604-:d:346163. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.