An event is not necessarily extreme simply because it is rare: it must also involve a quantifiable value that can be "small" or "large." Conversely, every extreme event is rare, in the sense that it has a low probability of occurring. Seeing a black swan is therefore a rare event, but not an extreme one.
Extreme events are difficult to model because, by definition, data are scarce or even nonexistent! We must therefore build a model from very little data.
Extreme value theory provides a rigorous mathematical foundation for building statistical models that predict the magnitude and frequency of these extreme events. The earliest work in the field is credited to Nicolas Bernoulli (1687–1759) in his 1709 thesis. The first application, dating from 1914, concerned flood discharges. Since then, applications have proliferated, particularly in meteorology.
