urrayleigh function

UNU.RAN Rayleigh random variate generator

UNU.RAN random variate generator for the Rayleigh distribution with scale parameter scale. It also allows sampling from the truncated distribution.

[Special Generator] -- Sampling Function: Rayleigh.

urrayleigh(n, scale=1, lb = 0, ub = Inf)

Arguments

• n: size of required sample.
• scale: (strictly positive) scale parameter.
• lb: lower bound of (truncated) distribution.
• ub: upper bound of (truncated) distribution.

Details

If scale is omitted, it assumes the default value of 1.

The Rayleigh distribution with scale parameter scale

$= s$ has density

for $x \ge 0$ and $s > 0$.

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

See Also

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

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 (1994): Continuous Univariate Distributions, Volume 1. 2nd edition, John Wiley & Sons, Inc., New York. Chap.18, p.456.

Author(s)

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

Note

This function is a wrapper for the UNU.RAN class in .

Examples

## Create a sample of size 1000 from Rayleigh distribution with scale=1
x <- urrayleigh(n=1000,scale=1)