Statistical Tests for Extreme Precipitation Volumes
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 observa...
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| Format: | Article |
| Language: | English |
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MDPI AG
2019-07-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/7/7/648 |
| _version_ | 1818992345460244480 |
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| author | Victor Korolev Andrey Gorshenin Konstatin Belyaev |
| author_facet | Victor Korolev Andrey Gorshenin Konstatin Belyaev |
| author_sort | Victor Korolev |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-20T20:24:41Z |
| format | Article |
| id | doaj.art-1697057711c14fd6bc7bc33daea43dcd |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-12-20T20:24:41Z |
| publishDate | 2019-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-1697057711c14fd6bc7bc33daea43dcd2022-12-21T19:27:29ZengMDPI AGMathematics2227-73902019-07-017764810.3390/math7070648math7070648Statistical Tests for Extreme Precipitation VolumesVictor Korolev0Andrey Gorshenin1Konstatin Belyaev2Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, Moscow 119991, RussiaFaculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, Moscow 119991, RussiaFaculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, Moscow 119991, RussiaThe 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.https://www.mdpi.com/2227-7390/7/7/648wet periodstotal precipitation volumeasymptotic approximationextreme order statisticsrandom sample sizetesting statistical hypotheses |
| spellingShingle | Victor Korolev Andrey Gorshenin Konstatin Belyaev Statistical Tests for Extreme Precipitation Volumes Mathematics wet periods total precipitation volume asymptotic approximation extreme order statistics random sample size testing statistical hypotheses |
| title | Statistical Tests for Extreme Precipitation Volumes |
| title_full | Statistical Tests for Extreme Precipitation Volumes |
| title_fullStr | Statistical Tests for Extreme Precipitation Volumes |
| title_full_unstemmed | Statistical Tests for Extreme Precipitation Volumes |
| title_short | Statistical Tests for Extreme Precipitation Volumes |
| title_sort | statistical tests for extreme precipitation volumes |
| topic | wet periods total precipitation volume asymptotic approximation extreme order statistics random sample size testing statistical hypotheses |
| url | https://www.mdpi.com/2227-7390/7/7/648 |
| work_keys_str_mv | AT victorkorolev statisticaltestsforextremeprecipitationvolumes AT andreygorshenin statisticaltestsforextremeprecipitationvolumes AT konstatinbelyaev statisticaltestsforextremeprecipitationvolumes |