Extreme value theory or
extreme value analysis (
EVA) is a branch of
statistics dealing with the extreme
deviations from the
median of
probability distributions. It seeks to assess, from a given ordered
sample of a given random variable, the probability of events that are more extreme than any previously observed. Extreme value analysis is widely used in many disciplines, such as structural engineering, finance, earth sciences, traffic prediction, and geological engineering. For example, EVA might be used in the field of
hydrology to estimate the probability of an unusually large flooding event, such as the
100-year flood. Similarly, for the design of a
breakwater, a
coastal engineer would seek to estimate the 50-year wave and design the structure accordingly.