udgumbel function

UNU.RAN object for Gumbel distribution

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).

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.

Details

The Gumbel distribution function with location $l$ and scale $s$ is

for all $x$.

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

Returns

An object of class "unuran.cont".

See Also

unuran.cont.

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.

Author(s)

Josef Leydold and Wolfgang H"ormann unuran@statmath.wu.ac.at .

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)