Abstract
Understanding and quantifying the behaviour of river floods at extreme discharges has important applications in design of civil structures
such as river dikes. For design purposes, one is often interested in return periods that are substantially larger than the observation period.
THese estimates are often obtained using classical statistical methods. In this paper, a method based on Bayesian statistics is presented.
This approach enables us to use all available sources of information and to take statistical uncertainties into account as well.
Seven predictive probability distributions are considered for determining extreme quantiles of loads: the exponential, Rayleigh, normal, log-
normal, gamma, Weibull, and Gumbel. The presented method has been successfully applied to estimate extreme quantiles of discharges
and their return periods. Prior information based on historical floods is represented in terms of censored data and is then used to determine
informative prior distributions of the statistical parameters. This prior information can be updated with actual data to determine the posterior
informatino, and provides a rational basis for extrapolation. As an example, a Bayesian analysis of annual maximum discharges of the river
Rhine at Lobith is performed to assess extreme quantiles such as the design discharge.
