Extreme-value Statistics: Rudiments and applications

TL;DR

This paper reviews the theory of extreme-value statistics, illustrating its application to real-world problems like flood return periods, meteorite impact frequency, and supercentenarian longevity, emphasizing practical analysis methods.

Contribution

It provides a clear, application-oriented summary of extreme-value theory with detailed examples demonstrating its use in diverse real-world scenarios.

Findings

Flood return periods estimated using extreme-value theory

Meteorite impact frequency and severity analyzed

Longevity data of supercentenarians examined

Abstract

This study provides a summary of the theory which enables the analysis of extreme values, i.e., of measurements acquired from the observation of extraordinary/rare physical phenomena. The formalism is developed in a transparent way, tailored to the application to real-world problems. Three examples of the application of the theory are detailed: first, an old problem, relating to the return period of floods caused by the Rh{\^o}ne river, is revisited; second, the frequency of occurrence and the severity of meteorite impacts on the Earth are examined; the data, which are analysed in the third example, relate to the longevity of supercentenarians.