The GEV distribution function with parameters \(\code{location} = a\), \(\code{scale} = b\) and \(\code{shape} = s\) is
dist_gev(location, scale, shape)$$F(x) = \exp\left[-\{1+s(x-a)/b\}^{-1/s}\right]$$
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).
Jenkinson, A. F. (1955) The frequency distribution of the annual maximum (or minimum) of meteorological elements. Quart. J. R. Met. Soc., 81, 158–171.
gev
dist <- dist_gev(location = 0, scale = 1, shape = 0)