Probability distribution fitting: Difference between revisions

Revision as of 22:40, 9 January 2022

Revision as of 07:05, 25 June 2022

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The following techniques of distribution fitting exist:<ref>''Frequency and Regression Analysis''. Chapter 6 in: H.P.Ritzema (ed., 1994), ''Drainage Principles and Applications'', Publ. 16, pp. 175–224, International Institute for Land Reclamation and Improvement (ILRI), Wageningen, The Netherlands. {{ISBN|9070754339}}. Free download from the webpage [http://www.waterlog.info/articles.htm] under nr. 12, or directly as PDF : [http://www.waterlog.info/pdf/freqtxt.pdf]</ref>

*''Parametric methods'', by which the [[parameter]]s of the distribution are calculated from the data series.<ref>H. Cramér, "Mathematical methods of statistics" , Princeton Univ. Press (1946)</ref> The parametric methods are:

**[[methodMethod of moments (statistics)|methodMethod of moments]]

**[[maximumMaximum spacing estimation]]

**methodMethod of [[L-moment]]s<ref>{{cite journal | last=Hosking | first=J.R.M. | year=1990 | title=L-moments: analysis and estimation of distributions using linear combinations of order statistics | journal=Journal of the Royal Statistical Society, Series B | volume=52 | pages=105–124 | jstor=2345653}}</ref>

**[[Maximum likelihood]] method<ref>{{cite journal | last = Aldrich | first = John | title = R. A. Fisher and the making of maximum likelihood 1912–1922 | year = 1997 | journal = Statistical Science | volume = 12 | issue = 3 | pages = 162–176 | doi = 10.1214/ss/1030037906 | mr = 1617519 | ref = citeref Aldrich1997| doi-access = free }}</ref>

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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]] ]]

*''[[Plotting position]] plus [[Regression method''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>

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