Density, distribution function, quantile function and random
generation for the generalized extreme value (GEV) distribution
with location, scale and shape parameters.
Location, scale and shape parameters; the
shape argument cannot be a vector (must have length one).
log
Logical; if TRUE, the log density is returned.
lower.tail
Logical; if TRUE (default), probabilities are
P[X <= x],="" otherwise,="" p[x=""> x]
Value
dgev gives the density, pgev gives the
distribution function, qgev gives the quantile function,
and rgev generates random deviates.
Details
The GEV distribution function with parameters
$\code{loc} = a$, $\code{scale} = b$ and
$\code{shape} = s$ is
$$G(z) = \exp\left[-{1+s(z-a)/b}^{-1/s}\right]$$
for $1+s(z-a)/b > 0$, where $b > 0$.
If $s = 0$ the distribution is defined by continuity.
The parametric form of the GEV encompasses that of the Gumbel,
Frechet and reversed 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.