IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v7y2019i7p648-d249880.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/7/7/648/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/7/7/648/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Kotz, Samuel & Ostrovskii, I. V., 1996. "A mixture representation of the Linnik distribution," Statistics & Probability Letters, Elsevier, vol. 26(1), pages 61-64, January.
    2. 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.
    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 & 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.

    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. Yury Khokhlov & Victor Korolev & Alexander Zeifman, 2020. "Multivariate Scale-Mixed Stable Distributions and Related Limit Theorems," Mathematics, MDPI, vol. 8(5), pages 1-29, May.
    3. 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.
    4. Dexter Cahoy, 2012. "An estimation procedure for the Linnik distribution," Statistical Papers, Springer, vol. 53(3), pages 617-628, August.
    5. Halvarsson, Daniel, 2013. "On the Estimation of Skewed Geometric Stable Distributions," Ratio Working Papers 216, The Ratio Institute.
    6. Soltani, A.R. & Tafakori, L., 2013. "A class of continuous kernels and Cauchy type heavy tail distributions," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 1018-1027.
    7. 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.
    8. Michael L. Stein, 2021. "A parametric model for distributions with flexible behavior in both tails," Environmetrics, John Wiley & Sons, Ltd., vol. 32(2), March.
    9. Pakes, Anthony G., 1998. "Mixture representations for symmetric generalized Linnik laws," Statistics & Probability Letters, Elsevier, vol. 37(3), pages 213-221, March.
    10. Lekshmi, V. Seetha & Jose, K.K., 2006. "Autoregressive processes with Pakes and geometric Pakes generalized Linnik marginals," Statistics & Probability Letters, Elsevier, vol. 76(3), pages 318-326, February.
    11. Kozubowski, Tomasz J., 1998. "Mixture representation of Linnik distribution revisited," Statistics & Probability Letters, Elsevier, vol. 38(2), pages 157-160, June.
    12. 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.
    13. 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).

    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:7:y:2019:i:7:p:648-:d:249880. 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.