Generalized extreme-value distribution

Description

Distribution function and quantile function of the generalized extreme-value distribution.

Usage

cdfgev(x, para = c(0, 1, 0))
quagev(f, para = c(0, 1, 0))

Arguments

Details

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.

Value

cdfgev gives the distribution function; quagev gives the quantile function.

Note

The functions expect the distribution parameters in a vector, rather than as separate arguments as in the standard R distribution functions pnorm, qnorm, etc.

See Also

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,

Examples

# 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))

Results