13. Extreme Value Analysis

Rolf-Dieter Reiss and Michael Thomas
28 July 2004

The extreme (upper or lower) parts of a sample, such as

have exhibited an increasing risk potential during the last decades. This is the reason why the statistical analysis of extremes has become an important question in theory and practice.

We give an outline of the most important statistical models (extreme value (EV) and generalized Pareto (GP)) of tools for assessing the adequacy of the parametric models (mean excess functions) and of relevant statistical estimation procedures.

The parametric distributions are fitted to observed maxima, minima, intermediate data or peaks over thresholds and extrapolated to regions of interest, where only a few or no observations are available. Such an extrapolation is not possible when a nonparametric approach is utilized. It is evident that the choice of the parametric model is a crucial issue.

The statistical models and procedures are implemented as a part of the finance library, so one needs to load that library first by using the command

  library ("finance")