Extreme value theory with application to huge rainfalls

The analysis of extreme events, such as floods, earthquakes or sever windstorms, has grown of importance over the years, since forecasting the occurrence of such intense phenomena is useful for both risk management and mitigation. In this work, the statistical methods deriving from Extreme value theory are used to analyze rainfall measurements collected in the province of Genoa, as in the last fifty years the area has been hit by a series of flash floods that have caused considerable damages. After having exposed the classical approach of Extreme value analysis, some generalizations are presented. Such characterizations of extremes have been developed with the aim to include additional information when modelling rare events and are known as: the r Largest Order Statistics approach and Threshold exceedances model. As regards the application case, inference for distribution parameters is performed through maximum likelihood estimation, while goodness of fit procedures, such as diagnostic plots, are exploited in order to assess model accuracy.