Distribution function and quantile function
of the generalized extreme-value distribution.
Usage
cdfgev(x, para = c(0, 1, 0))
quagev(f, para = c(0, 1, 0))
Arguments
x
Vector of quantiles.
f
Vector of probabilities.
para
Numeric vector containing the parameters of the distribution,
in the order $\xi, \alpha, k$ (location, scale, shape).
Value
cdfgev gives the distribution function;
quagev gives the quantile function.
Details
The generalized extreme-value distribution with
location parameter $\xi$,
scale parameter $\alpha$ and
shape parameter $k$ has distribution function
$$F(x)=\exp(-\exp(-y))$$ where
$$y=-k^{-1}\log(1-k(x-\xi)/\alpha),$$
with $x$ bounded by $\xi+\alpha/k$
from below if $k<0$ and="" from="" above="" if="" $k="">0$,
and quantile function
$$x(F)=\xi-{\alpha\over k}(1-(-\log F)^k).$$
Extreme-value distribution types I, II and III (Gumbel, Frechet, Weibull)
correspond to shape parameter values
$k=0$, $k<0$ and="" $k="">0$ respectively.
See Also
cdfgum for the Gumbel (extreme-value type I) distribution.
cdfkap for the kappa distribution,
which generalizes the generalized extreme-value distribution.
cdfwei for the Weibull distribution,