Statistics of Extremes

Introduction

Statistics of extremes concerns the occurrence of rare events: catastrophic flooding due to very high tides or landslides following unusually heavy rain, structural failure of dams and bridges, massive earthquakes, stock market crashes, and so forth. It has applications in many domains of engineering, in meteorology, hydrology and other earth sciences, in telecommunications, in finance and insurance – indeed, in any domain in which major risks arise due to unusual events or combinations thereof. In applications the available data are often very limited in relation to the event of interest, so a key issue is the validity of extrapolation far into the tail of a distribution, based on data that are less extreme. This is usually formulated mathematically in terms of stability properties that reasonable models ought to possess, and these properties place strong restrictions on the families of distributions on which extrapolation should be based. The relevance of such properties...