Extreme value modelling applied in hydrology

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In designing flood-control structures, or in estimating flood damage, decisions are often made on the basis of a short sample of river flow measurements. A statistical frequency distribution is chosen to fit the measurements, and the fitted distribution is then used to estimate future floods. Many methods exist to fit distributions to data. Some of the distributions have a finite upper bound that is a function of the distribution parameters (shape, scale, etc.). Some distribution fitting methods may produce an estimate of this upper bound that is inconsistent with the observed data. This occurs when one or more sample observations exceed the upper bound of the estimated distribution. This makes the estimated upper bound unrealistic. We will investigate this inconsistency of some estimation methods with the observed data and examine its engineering risk consequences. We hope to establish improved guidelines for choosing between statistical distributions and fitting methods for hydrological risk analysis.