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Article

Statistical Tests for Extreme Precipitation Volumes

1
Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, Moscow 119991, Russia
2
Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, Moscow 119333, Russia
3
Hangzhou Dianzi University, Hangzhou 310018, China
4
P. P. Shirshov Institute of Oceanology of the Russian Academy of Sciences, Moscow 117997, Russia
*
Author to whom correspondence should be addressed.
Mathematics 2019, 7(7), 648; https://doi.org/10.3390/math7070648
Received: 24 June 2019 / Revised: 15 July 2019 / Accepted: 17 July 2019 / Published: 19 July 2019
(This article belongs to the Special Issue Stochastic Processes: Theory and Applications)
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. View Full-Text
Keywords: wet periods; total precipitation volume; asymptotic approximation; extreme order statistics; random sample size; testing statistical hypotheses wet periods; total precipitation volume; asymptotic approximation; extreme order statistics; random sample size; testing statistical hypotheses
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MDPI and ACS Style

Korolev, V.; Gorshenin, A.; Belyaev, K. Statistical Tests for Extreme Precipitation Volumes. Mathematics 2019, 7, 648. https://doi.org/10.3390/math7070648

AMA Style

Korolev V, Gorshenin A, Belyaev K. Statistical Tests for Extreme Precipitation Volumes. Mathematics. 2019; 7(7):648. https://doi.org/10.3390/math7070648

Chicago/Turabian Style

Korolev, Victor, Andrey Gorshenin, and Konstatin Belyaev. 2019. "Statistical Tests for Extreme Precipitation Volumes" Mathematics 7, no. 7: 648. https://doi.org/10.3390/math7070648

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