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Statistical Tests for Extreme Precipitation Volumes

Author

Listed:
  • Victor Korolev

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

  • Andrey Gorshenin

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

  • Konstatin Belyaev

    (Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, Moscow 119991, Russia
    P. P. Shirshov Institute of Oceanology of the Russian Academy of Sciences, Moscow 117997, Russia)

Abstract

The analysis of the real observations of precipitation based on the novel statistical approach using the negative binomial distribution as a model for describing the random duration of a wet period is considered and discussed. The study shows that this distribution fits very well to the real observations and generalized standard methods used in meteorology to detect an extreme volume of precipitation. It also provides a theoretical base for the determination of asymptotic approximations to the distributions of the maximum daily precipitation volume within a wet period, as well as the total precipitation volume over a wet period. The paper demonstrates that the relation of the unique precipitation volume, having the gamma distribution, divided by the total precipitation volume taken over the wet period is given by the Snedecor–Fisher or beta distributions. It allows us to construct statistical tests to determine the extreme precipitations. Within this approach, it is possible to introduce the notions of relatively and absolutely extreme precipitation volumes. An alternative method to determine an extreme daily precipitation volume based on a certain quantile of the tempered Snedecor–Fisher distribution is also suggested. The results of the application of these methods to real data are presented.

Suggested Citation

  • Victor Korolev & Andrey Gorshenin & Konstatin Belyaev, 2019. "Statistical Tests for Extreme Precipitation Volumes," Mathematics, MDPI, vol. 7(7), pages 1-20, July.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:7:p:648-:d:249880
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    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. Kotz, Samuel & Ostrovskii, I. V., 1996. "A mixture representation of the Linnik distribution," Statistics & Probability Letters, Elsevier, vol. 26(1), pages 61-64, January.
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    Cited by:

    1. 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.

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