Rational Approach to Comparison of Flood Distributions by Simulation

A nonparametric Bayesian simulation procedure, Pólya resampling, is presented for comparing statistical distributions D and estimation methods E for at-site flood frequency analysis. The methodology does not rely on the hypothesis of a parent distribution and compares the models on the basis of expected cost. It is applied to the Québec-Ontario region. The statistical distribution minimizing expected cost depends mainly on the ratio of underestimation to overestimation costs. When these costs are similar, the gamma distribution performs well. When overestimation costs are more important, the normal distribution minimizes expected cost. And when underestimation costs are larger, the Gumbel distribution is preferred. However, this only tells us that the systematic use of these distributions is preferable to the systematic use of other distributions considered in the study. A dynamic procedure, which selects a D/E combination on the basis of some sample statistics, may give better results. In particular, a simple dynamic procedure based on the observed coefficients of variation and skewness is shown to outperform the gamma and Gumbel distributions for extrapolation when underestimation and overestimation costs are similar.