Statistical Modelling of Extremes with Distributions of Fréchet and Gumbel: Parameter Estimation and Demonstration of Meteorological Applications
The estimation of the Cumulative Distribution Function (CDF) of data sets of random variables is a fundamental goal in the statistical modelling of extreme natural and technological accidents. Various geophysical events such as drought, floods, avalanches and heavy precipitation are a prerequisite f...
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| Format: | Article |
| Language: | English |
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Bulgarian Academy of Sciences
2018-03-01
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| Series: | International Journal Bioautomation |
| Subjects: | |
| Online Access: | http://www.biomed.bas.bg/bioautomation/2018/vol_22.1/files/22.1_03.pdf |
| _version_ | 1817989322924621824 |
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| author | Hristo Chervenkov Krastina Malcheva |
| author_facet | Hristo Chervenkov Krastina Malcheva |
| author_sort | Hristo Chervenkov |
| collection | DOAJ |
| description | The estimation of the Cumulative Distribution Function (CDF) of data sets of random variables is a fundamental goal in the statistical modelling of extreme natural and technological accidents. Various geophysical events such as drought, floods, avalanches and heavy precipitation are a prerequisite for serious damage and economic losses, and therefore the comprehensive knowledge of their risk of occurrence, repetition periods and return levels is crucial for the planning and elaboration of mitigation strategies. The paper describes step-by-step the derivation of the parameters of the Fréchet and Gumbel CDFs, which form together with the Weibull one the Generalized Extreme Value (GEV) distribution family and are widely used for statistical modelling of extreme events. Two methods for estimation of the CDF-parameters are considered: least-square estimation and maximum-likelihood estimation. The developed and freely-available source code, written in FORTRAN 90/95, enhances the practical value of the presented work. The possibilities of the proposed approach for climatological applications are demonstrated by examples with time series of point measurements and gridded data sets. |
| first_indexed | 2024-04-14T00:44:44Z |
| format | Article |
| id | doaj.art-d92e1b72dc4742ed825fa3952e584afb |
| institution | Directory Open Access Journal |
| issn | 1314-1902 1314-2321 |
| language | English |
| last_indexed | 2024-04-14T00:44:44Z |
| publishDate | 2018-03-01 |
| publisher | Bulgarian Academy of Sciences |
| record_format | Article |
| series | International Journal Bioautomation |
| spelling | doaj.art-d92e1b72dc4742ed825fa3952e584afb2022-12-22T02:22:04ZengBulgarian Academy of SciencesInternational Journal Bioautomation1314-19021314-23212018-03-01221213810.7546/ijba.2018.22.1.21-38Statistical Modelling of Extremes with Distributions of Fréchet and Gumbel: Parameter Estimation and Demonstration of Meteorological ApplicationsHristo Chervenkov0Krastina MalchevaDepartment of Meteorology, National Institute of Meteorology and Hydrology, Bulgarian Academy of SciencesThe estimation of the Cumulative Distribution Function (CDF) of data sets of random variables is a fundamental goal in the statistical modelling of extreme natural and technological accidents. Various geophysical events such as drought, floods, avalanches and heavy precipitation are a prerequisite for serious damage and economic losses, and therefore the comprehensive knowledge of their risk of occurrence, repetition periods and return levels is crucial for the planning and elaboration of mitigation strategies. The paper describes step-by-step the derivation of the parameters of the Fréchet and Gumbel CDFs, which form together with the Weibull one the Generalized Extreme Value (GEV) distribution family and are widely used for statistical modelling of extreme events. Two methods for estimation of the CDF-parameters are considered: least-square estimation and maximum-likelihood estimation. The developed and freely-available source code, written in FORTRAN 90/95, enhances the practical value of the presented work. The possibilities of the proposed approach for climatological applications are demonstrated by examples with time series of point measurements and gridded data sets.http://www.biomed.bas.bg/bioautomation/2018/vol_22.1/files/22.1_03.pdfFréchet and Gumbel distributionCDF-parametersLeast-square estimationMaximum-likelihood estimationFree source code |
| spellingShingle | Hristo Chervenkov Krastina Malcheva Statistical Modelling of Extremes with Distributions of Fréchet and Gumbel: Parameter Estimation and Demonstration of Meteorological Applications International Journal Bioautomation Fréchet and Gumbel distribution CDF-parameters Least-square estimation Maximum-likelihood estimation Free source code |
| title | Statistical Modelling of Extremes with Distributions of Fréchet and Gumbel: Parameter Estimation and Demonstration of Meteorological Applications |
| title_full | Statistical Modelling of Extremes with Distributions of Fréchet and Gumbel: Parameter Estimation and Demonstration of Meteorological Applications |
| title_fullStr | Statistical Modelling of Extremes with Distributions of Fréchet and Gumbel: Parameter Estimation and Demonstration of Meteorological Applications |
| title_full_unstemmed | Statistical Modelling of Extremes with Distributions of Fréchet and Gumbel: Parameter Estimation and Demonstration of Meteorological Applications |
| title_short | Statistical Modelling of Extremes with Distributions of Fréchet and Gumbel: Parameter Estimation and Demonstration of Meteorological Applications |
| title_sort | statistical modelling of extremes with distributions of frechet and gumbel parameter estimation and demonstration of meteorological applications |
| topic | Fréchet and Gumbel distribution CDF-parameters Least-square estimation Maximum-likelihood estimation Free source code |
| url | http://www.biomed.bas.bg/bioautomation/2018/vol_22.1/files/22.1_03.pdf |
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