Runuran (version 0.21.0)

udgumbel: UNU.RAN object for Gumbel distribution

Description

Create UNU.RAN object for a Gumbel (Extreme value type I) distribution location parameter location and scale parameter scale. [Distribution] -- Gumbel (Extreme value type I).

Usage

udgumbel(location=0, scale=1, lb=-Inf, ub=Inf)

Arguments

location

location parameter.

scale

(strictly positive) scale parameter.

lb

lower bound of (truncated) distribution.

ub

upper bound of (truncated) distribution.

Value

• An object of class "unuran.cont".

Details

The Gumbel distribution function with location $l$ and scale $s$ is $$F(x) = \exp(-\exp(-\frac{x-l}{s}))$$ for all $x$.

The domain of the distribution can be truncated to the interval (lb,ub).

References

N.L. Johnson, S. Kotz, and N. Balakrishnan (1995): Continuous Univariate Distributions, Volume 2. 2nd edition, John Wiley & Sons, Inc., New York. Chap. 22, p. 2.

See Also

unuran.cont.

Examples

## Create distribution object for Gumbel distribution
distr <- udgumbel()
## Generate generator object; use method PINV (inversion)
gen <- pinvd.new(distr)
## Draw a sample of size 100
x <- ur(gen,100)