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))
Value
cdfgum gives the distribution function;
quagum gives the quantile function.
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).
Details
The Gumbel distribution with
location parameter \(\xi\) and
scale parameter \(\alpha\)
has distribution function
$$F(x)=\exp[-\exp\lbrace-(x-\xi)/\alpha\rbrace]$$
and quantile function
$$x(F)=\xi-\alpha\log(-\log F).$$
See Also
cdfgev for the generalized extreme-value distribution,
which generalizes the Gumbel distribution.