Bayesian Estimation of Quantiles for the Purpose of Flood Prevention

In this paper, the problem of Bayesian estimation of flood quantiles is studied. Bayes estimators of the optimal dyke height under symmetric and asymmetric loss are investigated when the annual maximum sea water levels are exponentially distributed with unknown value of the mean. Three types of loss functions are considered: (i) linear loss, (ii) squared-error loss, and (iii) linex loss. In order to properly account for the statistical uncertainty in the mean, a modified linex loss function is to be preferred. This new modified linex loss function is derived from the economic dyke heigthening problem of Van Dantzig. Since the loss function is based on a benefit-cost analysis, its parameters have a clear economic significance. Introduction In statistical analysis of civil engineering data such as water levels, wave heights, soil parameters, etc., many attempts have been made to establish what kind of fitting method is preferable for the parameter estimation of a probability distribution in order to estimate the q-quantile, i.e. the value with a probability of exceedance equal to q (where q is usually very small, in the order of 10 to 10). Recent research on this subject can be found in, for example, Yamaguchi (1997), Fortin et al. (1997), Burcharth and Liu (1994), and Van Gelder (1996). The main idea in their work is to generate random samples from a chosen probability distribution using Monte Carlo simulation, and to investigate the advantage of a certain parameter estimation method over the other method which is based on the viewpoint of bias and variance of the q-quantile. The estimation method with the 1 HKV Consultants, P.O. Box 2120, 8203 AC Lelystad, The Netherland, and Delft University of Technology, Faculty of Mathematics and Computer Science, P.O. Box 5031, 2600 GA Delft, The Netherlands, E-mail: [email protected]. 2 Delft University of Technology, Faculty of Civil Engineering, P.O. Box 5048, 2600 GA Delft, The Netherlands, E-mail: [email protected].