Extreme value analysis deals with the statistical modeling and analysis of extremal observations in a sample, in univariate, multivariate as well as in infinite dimensional space. The restriction of the statistical analysis to the extremal observations is justified by the fact that this part of the data can be of outstanding importance. Floods, hurricanes, extreme claim sizes, etc. obviously exhibit a large risk scenario.
Extremal observations may be defined in different ways, either as maxima or as exceedances above high thresholds. The first approach led to the "annual maxima method", ruled by extreme value distributions. It is well-known that exceedances over high thresholds can reasonably be modeled only by a generalized Pareto distribution. However only in recent years has this alternative approach to the traditional annual maxima method been widely spread outside the academic world as well. Extreme value analysis has its pecularities and cannot be looked in isolation, but instead it must be linked to other branches of statistics as well.