Runuran (version 0.40)

urextremeII: UNU.RAN Extreme value type II (Frechet-type) random variate generator

Description

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

[Special Generator] -- Sampling Function: Frechet (extreme value type II).

Usage

urextremeII(n, shape, location=0, scale=1, lb=location, ub=Inf)

Arguments

n

size of required sample.

shape

(strictly positive) shape parameter.

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 Frechet distribution function with shape \(k\), location \(l\) and scale \(s\) is $$ F(x) = \exp(-(\frac{x-l}{s})^{-k}) $$ for \(x \ge l\).

The generation algorithm uses fast numerical inversion. The parameters lb and ub can be used to generate variates from the Frechet 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 <- urextremeII(n=1000,shape=2)