Probability distribution fitting: Difference between revisions

Revision as of 04:10, 8 November 2022

Revision as of 22:27, 24 November 2022

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| bgcolor="white" | ''For example, the parameter <math>\mu</math> (the'' ''[[expected value|expectation]]) can be estimated by the [[Arithmetic mean|mean]] of the data and the parameter <math>\sigma^2</math> (the [[variance]]) can be estimated from the [[standard deviation]] of the data. The mean is found as <math display="inline">m=\sum{X}/n</math>, where <math>X</math> is the data value and <math>n</math> the number of data, while the standard deviation is calculated as <math display="inline">s = \sqrt{\frac{1}{n-1} \sum{(X-m)^2}}</math>. With these parameters many distributions, e.g. the normal distribution, are completely defined.''

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[[File:FitGumbelDistr.tif|thumb|220px|Cumulative Gumbel distribution fitted to maximum one-day October rainfalls in [[SurinamSuriname]] by the regression method with added '''[[confidence band]]''' using [[CumFreq|cumfreq]] ]]

*[[Plotting position]] plus [[Regression analysis]], 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 name="gen">Software for Generalized and Composite Probability Distributions. International Journal of Mathematical and Computational Methods, 4, 1-9 [https://www.iaras.org/iaras/home/caijmcm/software-for-generalized-and-composite-probability-distributions] or [https://www.waterlog.info/pdf/MathJournal.pdf]</ref>