Generalized extreme-value distribution
Distribution function and quantile function of the generalized extreme-value distribution.
cdfgev(x, para = c(0, 1, 0)) quagev(f, para = c(0, 1, 0))
x |
Vector of quantiles. |
f |
Vector of probabilities. |
para |
Numeric vector containing the parameters of the distribution, in the order xi, alpha, k (location, scale, shape). |
The generalized extreme-value distribution with location parameter xi, scale parameter alpha and shape parameter k has distribution function
F(x) = exp(-exp(-y))
where
y = (-1/k) log(1-k(x-xi)/alpha) ,
with x bounded by xi+alpha/k from below if k<0 and from above if k>0, and quantile function
x(F) = xi + alpha (1 - (-log(F))^k) / k .
Extreme-value distribution types I, II and III (Gumbel, Frechet, Weibull) correspond to shape parameter values k=0, k<0 and k>0 respectively.
cdfgev gives the distribution function;
quagev gives the quantile function.
The functions expect the distribution parameters in a vector,
rather than as separate arguments as in the standard R
distribution functions pnorm, qnorm, etc.
cdfgum for the Gumbel (extreme-value type I) distribution.
cdfkap for the kappa distribution,
which generalizes the generalized extreme-value distribution.
cdfwei for the Weibull distribution,
# Random sample from the generalized extreme-value distribution # with parameters xi=0, alpha=1, k=-0.5. quagev(runif(100), c(0,1,-0.5))
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