The Quantile Estimation of the Maxima of Sea Levels

The hydrological modeling has become an intensively studied subject in recent years. One of the most significant problems concerning this issue is to provide the mathematical and statistical tools, which allow to forecast extreme hydrological events, such as severe sea or river floodings. The extreme events on water have huge social and economic impact on the affected areas. Due to these reasons, each country has to protect itself against the flood danger, and consequently, the designing of reliable flood defences is of great importance to the safety of the region. For example, the sea dikes along the Dutch coastline are designed to withstand floods, which may occur once every 10 000 years. It means that the height of the dike is determined in such a way that the probability of the event that there is a flood in a given year equals 10. The computation of such the height level requires the estimation of the corresponding quantiles of the distributions of certain maxima of sea levels. In our paper, we present the procedures, which lead to the estimation of such the quantiles. We are mainly concerned with the interval estimation; in this context, we present the frequentistic and Bayesian approaches in constructing the desired confidence intervals.