Runuran (version 0.40)

urextremeI: UNU.RAN Extreme value type I (Gumbel-type) random variate generator

Description

UNU.RAN random variate generator for the Extreme value type I (Gumbel-type) distribution with location parameter location and scale parameter scale. It also allows sampling from the truncated distribution.

[Special Generator] -- Sampling Function: Gumbel (extreme value type I).

Usage

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

Arguments

n

size of required sample.

location

location parameter.

scale

(strictly positive) scale parameter.

lb

lower bound of (truncated) distribution.

ub

upper bound of (truncated) distribution.

Author

Josef Leydold and Wolfgang H\"ormann .

Details

If location or scale are not specified, they assume the default values of 0 and 1 respectively.

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

The generation algorithm uses fast numerical inversion. The parameters lb and ub can be used to generate variates from the Gumbel distribution truncated to the interval (lb,ub).

References

W. H\"ormann, J. Leydold, and G. Derflinger (2004): Automatic Nonuniform Random Variate Generation. Springer-Verlag, Berlin Heidelberg.

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

runif and .Random.seed about random number generation and unuran for the UNU.RAN class.

Examples

## Create a sample of size 1000
x <- urextremeI(n=1000)