The extreme value type I distribution has two forms. One is based on the smallest extreme and the other is based on the largest extreme. We call these the minimum and maximum cases, respectively. Formulas and plots for both cases are given. The extreme value type I distribution is also referred to as the Gumbel distribution.

The general formula for the probability density function of the Gumbel (maximum) distribution is

f(x,alpha,beta) = exp ( (alpha-x) / beta-exp (alpha-x) / beta) / beta)

support -Inf ⇐ x ⇐ Inf