Tales of the Wakeby Tail and Alternatives When Modelling Extreme Floods

Abstract

Estimation of return levels, based on extreme-value distributions, is of importance in the earth and environmental sciences. The selection of an appropriate probability distribution is crucial. The Wakeby distribution has shown to be an interesting alternative. By simulation studies, we investigate by various means of minimum distance to distinguish between common distributions when modelling extreme events in hydrology. Estimation of parameters is performed by L-moments. Moreover, time series of annual maximum floods from major unregulated rivers in Northern Sweden were analysed with respect to fitting an appropriate distribution. The results of the simulation study shows that the Wakeby distribution has the best fit of the tail for a wide range of sample sizes. For the analysis of extreme floods, the Wakeby distribution is in the majority of cases the best fit by means of minimum distance. However, when considering estimation of return levels by competing distributions, results can vary considerably for longer return periods.