Bayes Estimates of Flood Quantiles using the Generalised Gamma Distribution∗

In this paper, a Bayesian approach is proposed to estimate flood quantiles while taking statistical uncertainties into account. Predictive exceedance probabilities of annual maximum discharges are obtained using the threeand fourparameter generalised gamma distribution (without and with location parameter respectively). 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 is then updated to the posterior joint distribution by using Bayes’ theorem. An advantage is that the generalised gamma distribution fits well with the stagedischarge rating curve being an approximate power law between water level and discharge. Furthermore, since the generalised gamma distribution has three or four parameters, it is flexible in fitting 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 example, a Bayesian analysis of annual maximum discharges of the Rhine River at Lobith is performed to determine flood quantiles including their uncertainty intervals. The generalised gamma distribution can also be applied in lifetime and reliability analysis.