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[[File:FitGumbelDistr.tif|thumb|220px|Cumulative Gumbel distribution fitted to maximum one-day October rainfalls in [[Surinam]] by the regression method with added '''[[confidence band]]''' using [[CumFreq|cumfreq]] ]]
*''Regression method'', using a transformation of the [[cumulative distribution function]] so that a [[linear relation]] is found between the [[cumulative probability]] and the values of the data, which may also need to be transformed, depending on the selected probability distribution. In this method the cumulative probability needs to be estimated by the [[plotting position]] <ref>{{cite journal | last = Oosterbaan | first = R.J. | title = Software for Generalized and Composite Probability Distributions2 | year = 2019 | journal = International Journal of Mathematical and Computational Methods | volume = 4 | pages = 1-9 }} [https://www.iaras.org/iaras/home/caijmcm/software-for-generalized-and-composite-probability-distributions]</ref>.
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| bgcolor="white" |For example, the cumulative [[Gumbel distribution]] can be linearized to <math>Y=aX+b</math>, where <math>X</math> is the data variable and <math>Y=-\ln(-\ln P)</math>, with <math>P</math> being the cumulative probability, i.e. the probability that the data value is less than <math>X</math>. Thus, using the [[plotting position]] for <math>P</math>, one finds the parameters <math>a</math> and <math>b</math> from a linear regression of <math>Y</math> on <math>X</math>, and the Gumbel distribution is fully defined.
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