Extreme Events in Hydrology: an approach using Exploratory Statistics and the Generalized Pareto Distribution. Performances and properties of the GPD estimators with outliers and rounded-off datasets

Two large databases of daily cumulated rainfall are checked with the tools of the Exploratory statistics. The analysis allows to discover not common artefacts in the first database (rounding-off of data with different rounding-off rules) and several errors in the other one. The best statistical model to fit data is selected using the L-Moments ratio diagram as a tool to explore the accommodation of each dataset to other alternative models. This tool suggests the Generalized Pareto Distribution as the best statistical model for this data, but the application of this distribution requires an estimate of the optimal threshold for each dataset. A detailed analysis of the present techniques for the optimal threshold selection is performed and a new approach based on quantile sums is proposed. Furthermore the performances of the GPD parameters estimators are checked for robustness against spurious rounded-off data and severe outliers.