Gumbel (extreme-value type I) distribution

Description

Distribution function and quantile function of the Gumbel distribution.

Usage

cdfgum(x, para = c(0, 1))
quagum(f, para = c(0, 1))

Arguments

Details

The Gumbel distribution with location parameter xi and scale parameter alpha has distribution function

F(x) = exp(-exp(-(x-xi)/alpha))

and quantile function

x(F) = xi - alpha log(-log F) .

Value

cdfgum gives the distribution function; quagum 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

cdfgev for the generalized extreme-value distribution, which generalizes the Gumbel distribution.

Examples

# Random sample from the Gumbel distribution with parameters xi=0, alpha=3.
quagum(runif(100), c(0,3))

Results