dist_gev: The Generalized Extreme Value Distribution

In distributional: Vectorised Probability Distributions

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 a of the GEV distribution.
scale	the scale parameter b of the GEV distribution.
shape	the shape parameter s of the GEV distribution.

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

gev

Examples

dist <- dist_gev(location = 0, scale = 1, shape = 0)

distributional documentation built on Sept. 17, 2024, 9:11 a.m.