dist_gev {distributional} | R Documentation |
The Generalized Extreme Value Distribution
Description
The GEV distribution function with parameters \code{location} = a
,
\code{scale} = b
and \code{shape} = s
is
Usage
dist_gev(location, scale, shape)
Arguments
location |
the location parameter |
scale |
the scale parameter |
shape |
the shape parameter |
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).
References
Jenkinson, A. F. (1955) The frequency distribution of the annual maximum (or minimum) of meteorological elements. Quart. J. R. Met. Soc., 81, 158–171.
See Also
Examples
dist <- dist_gev(location = 0, scale = 1, shape = 0)