logical; if TRUE (default)
probabilities are \(P(X \le x)\) otherwise, \(P(X > x)\).
log, log.p
logical; if TRUE, probabilities p are
given as log(p).
Value
dGEV() computes the density, pGEV() the distribution
function, qGEV() the quantile function and rGEV() random
variates of the generalized extreme value distribution.
Details
The distribution function of the generalized extreme value
distribution is given by
$$F(x) = \cases{
\exp(-(1-\xi(x-\mu)/\sigma)^{-1/\xi}),&if $\xi\neq 0,\ 1+\xi(x-\mu)/\sigma>0$,\cr
\exp(-e^{-(x-\mu)/\sigma}),&if $\xi = 0$,\cr}$$
where \(\sigma>0\).
References
McNeil, A. J., Frey, R., and Embrechts, P. (2015).
Quantitative Risk Management: Concepts, Techniques, Tools.
Princeton University Press.