GEV | R Documentation |
Density, distribution function, quantile function and random variate generation for the generalized extreme value distribution (GEV).
dGEV(x, shape, loc = 0, scale = 1, log = FALSE) pGEV(q, shape, loc = 0, scale = 1, lower.tail = TRUE, log.p = FALSE) qGEV(p, shape, loc = 0, scale = 1, lower.tail = TRUE, log.p = FALSE) rGEV(n, shape, loc = 0, scale = 1)
x, q |
vector of quantiles. |
p |
vector of probabilities. |
n |
number of observations. |
shape |
GEV shape parameter xi, a real. |
loc |
GEV location parameter mu, a real. |
scale |
GEV scale parameter sigma, a positive real. |
lower.tail |
|
log, log.p |
logical; if |
The distribution function of the generalized extreme value distribution is given by
F(x) = exp(-(1-xi(x-mu)/sigma)^{-1/xi}) if xi != 0, 1+xi*(x-mu)/sigma>0 and exp(-e^{-(x-mu)/sigma}) if xi = 0,
where sigma>0.
dGEV()
computes the density, pGEV()
the distribution
function, qGEV()
the quantile function and rGEV()
random
variates of the generalized extreme value distribution.
Marius Hofert
McNeil, A. J., Frey, R., and Embrechts, P. (2015). Quantitative Risk Management: Concepts, Techniques, Tools. Princeton University Press.
## Basic sanity checks plot(pGEV(rGEV(1000, shape = 0.5), shape = 0.5)) # should be U[0,1] curve(dGEV(x, shape = 0.5), from = -3, to = 5)
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