Extreme value theory

This article is about the statistical theory. For the result in calculus, see extreme value theorem.
Extreme value theory is used to model the risk of extreme, rare events, such as the 1755 Lisbon earthquake.

Extreme value theory or extreme value analysis (EVA) is the study of extremes in statistical distributions.

It is widely used in many disciplines, such as structural engineering, finance, economics, 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.