Probability distribution fitting: Difference between revisions

Revision as of 11:36, 22 October 2019

Revision as of 01:11, 13 January 2020

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==Composite distributions==

[[File:SanLor.jpg|thumb|left|Composite (discontinuous) distribution with confidence belt <ref>Intro to composite probability distributions [https://www.waterlog.info/composite.htm Intro to composite probability distributions]</ref> ]]

The option exists to use two different probability distributions, one for the lower data range, and one for the higher like for example the [[Laplace distribution]]. The ranges are separated by a break-point. The use of such composite (discontinuous) probability distributions can be opportune when the data of the phenomenon studied were obtained under two sets different conditions. <ref>''Software for Generalized and Composite Probability Distributions''. In: International Journal of Mathematical and Computational Methods, January 2019. On line: [https://www.iaras.org/iaras/filedownloads/ijmcm/2019/001-0001(2019).pdf] </ref>

== Uncertainty of prediction ==

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With the binomial distribution one can obtain a [[confidence interval]] of the prediction. Such an interval also estimates the risk of failure, i.e. the chance that the predicted event still remains outside the confidence interval. The confidence or risk analysis may include the [[return period]] ''T=1/Pe'' as is done in [[hydrology]].

[[File:CumList.png|thumb|left|List of probability distributions ranked by goodness of fit. <ref>Software for probability distribution fitting. [https://www.waterlog.info/cumfreq.htm] Software for probability distribution fitting]</ref>]]

[[File:GEVdistrHistogr+Density.png|thumb|220px|Histogram and probability density of a data set fitting the [[GEV distribution]] ]]