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.