The Frequentistic and Bayesian quantile estimation for the maxima of sea levels

• Published in: Model assisted statistics and applications 2014, Vol.9 (4), p.325-342
• Main Authors: Dudziński, Marcin, Furmańczyk, Konrad
• Format: Article
• Language: English
• ISSN: 1574-1699; 1875-9068
• DOI: 10.3233/MAS-140304

Hydrological modelling has become an intensively studied subject in recent years. One of the most significant problems concerning this issue is to provide mathematical and statistical tools, which allow to forecast extreme hydrological events, such as severe sea or river floodings. In particular, the estimation of flood quantiles is often needed in hydrological design to construct reliable flood defences. In our paper, we establish procedures leading to the interval estimation of the quantiles of the maxima of sea levels. We mainly focus on the quantile estimation for the distributions of the 3-day maxima of sea levels, although some general patterns involving the quantile estimation for the distributions of the m-day maxima of sea levels, where m>3, are also delivered. The introduced estimation scheme uses the Peaks over Threshold (POT) approach as one of theoretical frameworks. We propose the Frequentistic and Bayesian approaches in the constructions of our confidence intervals (CIs). The choice of optimal threshold in the presented method based on the POT approach is discussed as well. The coverage probabilities for the corresponding CIs are also computed.