$$F(x) = \exp\left[-\{1+s(x-a)/b\}^{-1/s}\right]$$
for \(1+s(x-a)/b > 0\), where \(b > 0\). If \(s = 0\) the distribution
is defined by continuity, giving
$$F(x) = \exp\left[-\exp\left(-\frac{x-a}{b}\right)\right]$$
The support of the distribution is the real line if \(s = 0\),
\(x \geq a - b/s\) if \(s \neq 0\), and
\(x \leq a - b/s\) if \(s < 0\).
The parametric form of the GEV encompasses that of the Gumbel, Frechet and
reverse Weibull distributions, which are obtained for \(s = 0\),
\(s > 0\) and \(s < 0\) respectively. It was first introduced by
Jenkinson (1955).