Probability distribution fitting: Difference between revisions

Revision as of 02:00, 15 April 2020

Revision as of 20:33, 31 August 2020

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An estimate of the uncertainty in the first and second case can be obtained with the [[Binomial distribution|binomial probability distribution]] using for example the probability of exceedance ''Pe'' (i.e. the chance that the event ''X'' is larger than a reference value ''Xr'' of ''X'') and the probability of non-exceedance ''Pn'' (i.e. the chance that the event ''X'' is smaller than or equal to the reference value ''Xr'', this is also called [[cumulative probability]]). In this case there are only two possibilities: either there is exceedance or there is non-exceedance. This duality is the reason that the binomial distribution is applicable.

With the binomial distribution one can obtain a [[confidenceprediction 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>[https://www.waterlog.info/cumfreq.htm Software for probability distribution fitting]</ref>]]