cdfgum: Gumbel (extreme-value type I) distribution
Description
Distribution function and quantile function
of the Gumbel distribution.
Usage
cdfgum(x, para = c(0, 1))
quagum(f, para = c(0, 1))
Arguments
x
Vector of quantiles.
f
Vector of probabilities.
para
Numeric vector containing the parameters of the distribution,
in the order $\xi, \alpha$ (location, scale).
Value
cdfgum gives the distribution function;
quagum gives the quantile function.
Details
The Gumbel distribution with
location parameter $\xi$ and
scale parameter $\alpha$
has distribution function
$$F(x)=\exp(-\exp(-(x-\xi)/\alpha))$$
and quantile function
$$x(F)=\xi-\alpha\log(-\log(F)).$$
See Also
cdfgev for the generalized extreme-value distribution,
which generalizes the Gumbel distribution.