On the tails of distributions of annual peak flow

Abstract

This study discusses an application of heavy-tailed distributions to modelling of annual peak flows in general and of Polish data sets in particular. One- and two-shape parameter heavy-tailed distributions are obtained by transformations of random variables. The correct selection of a flood frequency model with emphasis on heavy-tailed distribution discrimination is then discussed. If a distribution is wrongly assumed, the error, in the upper quantile, arising as a result, depends on the method of parameter estimation and is shown analytically for three methods. Asymptotic and sampling values (got by simulation) were assessed for the pair log-Gumbel (LG) as a false distribution and log-normal (LN) as a true distribution. Comparing the upper quantiles of various distributions with the same values of moments, it is found that heavy-tailed distributions do not consistently provide higher flood frequency estimates than do soft-tailed distributions. Based on L-moment ratio diagrams and the test of linearity on log–log plots, it is concluded that Polish datasets of annual peak flows should be modelled using soft-tailed distributions, such as the three-parameter Inverse Gaussian, rather than heavy-tailed distributions.