The GEV distribution function with parameters \(\code{location} = a\), \(\code{scale} = b\) and \(\code{shape} = s\) is
Details
$$F(x) = \exp\left[-\{1+s(x-a)/b\}^{-1/s}\right]$$
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).