urrayleigh: UNU.RAN Rayleigh random variate generator
Description
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.
Usage
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
$=\sigma$ has density
$$f(x) = \frac{1}{sigma^2} x \exp( -\frac{1}{2}(\frac{x}{sigma})^2 )$$
for $x \ge 0$ and $\sigma > 0$.
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).
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.
See Also
runif and .Random.seed about random number
generation and unuran for the UNU.RAN class.