Extreme value theory

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, actuarial science, 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. Two main approaches exist for practical extreme value analysis. The first method relies on deriving block maxima (minima) series as a preliminary step. In many situations it is customary and convenient to extract the annual maxima (minima), generating an annual maxima series (AMS). The second method relies on extracting, from a continuous record, the peak values reached for any period during which values exceed a certain threshold (falls below a certain threshold). This method is generally referred to as the peak over threshold method (POT). For AMS data, the analysis may partly rely on the results of the Fisher–Tippett–Gnedenko theorem, leading to the generalized extreme value distribution being selected for fitting.