The importance of statistical uncertainties in selecting appropriate methods for estimation of extremes

Statistical uncertainties in the estimation of extremes are normally not well considered in present practice or even present research. This paper shows the application of extreme distributions to river variables with non negligible levels of uncertainty and presents an approach to deal with them. Four distribution types (Gumbel, Pearson III (log shifted Gamma), Lognormal and Generalised Pareto) are fitted to peaks over threshold or annual maxima data sets of river discharges. Piecewise exponential distributions are used to summarise the four distribution types and bootstrapping methods for quantifying the uncertainty in the design discharges. The paper furthermore presents relationships between probability density functions, convergence theorems and statistical tests to judge the goodness of fits.