User:Asitgoes/sandbox

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{{navbox | name = Distribution fitting software | title = Distribution fitting software | sate = Uncollapsed | bodyclass = hlist | list1 =

Uncertainty of prediction

Variations of nine return period curves of 50-year samples from a theoretical 1000 year record (base line), data from Benson

Uncertainty analysis with confidence belts using the binomial distribution

Predictions of occurrence based on fitted probability distributions are subject to uncertainty, which arises from the following conditions:

• The true probability distribution of events may deviate from the fitted distribution, as the observed data series may not be totally representative of the real probability of occurrence of the phenomenon due to random error
• The occurrence of events in another situation or in the future may deviate from the fitted distribution as this occurrence can also be subject to random error
• A change of environmental conditions may cause a change in the probability of occurrence of the phenomenon

An estimate of the uncertainty in the first and second case can be obtained with the 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), 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 this 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.