Estimation of Extreme Values, with Application to Uncertain Systems

Extreme events are defined as extreme high (or low) values of whatever statistics of the output of the system we are interested in. These values play an important role because they may correspond to abnormal or dangerous operating conditions. Classical statistical inference techniques provide a good description of central behaviour, but not of extreme events. This was our motivation for resorting to extreme-value theory, which provides a framework and tools to model these extreme events. We show in this paper how some of these tools can be used in the context of system reliability, and the resulting methodology is illustrated on an example of circuit design, representative of a wide new field of applications for extreme-value theory.