dist_gev {distributional} | R Documentation |
The GEV distribution function with parameters \code{location} = a
,
\code{scale} = b
and \code{shape} = s
is
dist_gev(location, scale, shape)
location |
the location parameter |
scale |
the scale parameter |
shape |
the shape parameter |
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.
dist <- dist_gev(location = 0, scale = 1, shape = 0)