Generalized Extreme Value Distribution: The Generalized Extreme Value Distribution
Description
Density, distribution function, quantile function and random
generation for the GP distribution with location equal to 'loc',
scale equal to 'scale' and shape equal to 'shape'.
logical; if TRUE (default), probabilities are \(\Pr[ X
\le x]\), otherwise, \(\Pr[X > x]\).
log
logical; if TRUE, probabilities p are given as log(p).
Value
If 'loc', 'scale' and 'shape' are not specified they assume the default
values of '0', '1' and '0', respectively.
The GEV distribution function for loc = \(u\), scale =
\(\sigma\) and shape = \(\xi\) is
$$G(x) = \exp\left[-\left\{1 + \xi \frac{x - u}{\sigma}
\right\}^{-1 / \xi} \right]$$
for \(1 + \xi ( x - u ) / \sigma > 0\)
and \(x > u\), where \(\sigma > 0\). If
\(\xi = 0\), the distribution is defined by continuity
corresponding to the Gumbel distribution.