The Three Extreme Value Distributions: An Introductory Review

TL;DR

This paper provides a clear, introductory overview of the three main types of extreme value distributions—Weibull, Fréchet, and Gumbel—and explains how sample data relate to these distributions, targeting the physics community.

Contribution

It offers a simple, compact guide on extreme value distributions, filling a gap for physicists and other scientists unfamiliar with this classification.

Findings

Clarifies the relationship between sample distributions and extreme value types.

Summarizes the three possible shapes of the distribution of maximum values.

Provides a practical guide for identifying the appropriate extreme value distribution.

Abstract

The statistical distribution of the largest value drawn from a sample of a given size has only three possible shapes: it is either a Weibull, a Fr\'echet or a Gumbel extreme value distributions. I describe in this short review how to relate the statistical distribution followed by the numbers in the sample to the associate extreme value distribution followed by the largest value within the sample. Nothing I present here is new. However, from experience, I have found that a simple and compact guide on this matter written for the physics community is missing.