Quantiles of Generalised Gamma Distributions from a Bayesian Point of View

In this paper, a Bayesian approach is proposed to estimate ood quan-tiles while taking the statistical uncertainties into account. Predictive excee-dence probabilities of annual maximum discharges are obtained using the three-parameter generalised gamma distribution. The parameters of this distribution are assumed to be random quantities rather than deterministic quantities and to have a prior joint probability distribution. On the basis of observations, this prior joint distribution can be updated to the posterior joint distribution by using Bayes' theorem. An advantage is that the generalised gamma distribution ts in well with the stage-discharge rating equation being an approximate power law between water level and discharge. Furthermore, since the generalised gamma distribution has three parameters, it is exible in tting data. Many well-known probability distributions, which are commonly used to estimate quantiles of hydrological random quantities, are special cases of the generalised gamma distribution. As an axample, a Bayesian analysis of annual maximum discharges of the Rhine at Lobith is performed to determine ood quantiles including their uncertainty intervals.