page_title: Probability distribution fitting
section_title: Uncertainty of prediction
hierarchical_section_title: Probability distribution fitting / Uncertainty of prediction
caption_attribution_description: English: Histrogram and probability density of a data set fitting the GEV distribution
context_page_description: Probability distribution fitting or simply distribution fitting is the fitting of a probability distribution to a series of data concerning the repeated measurement of a variable phenomenon.
  The aim of distribution fitting is to predict the probability or to forecast the frequency of occurrence of the magnitude of the phenomenon in a certain interval.
  There are many probability distributions of which some can be fitted more closely to the observed frequency of the data than others, depending on the characteristics of the phenomenon and of the distribution. The distribution giving a close fit is supposed to lead to good predictions.
  In distribution fitting, therefore, one needs to select a distribution that suits the data well.
context_section_description: 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) 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 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.
caption: Histogram and probability density of a data set fitting the GEV distribution
exif: {}