Runuran (version 0.40)

udrayleigh: UNU.RAN object for Rayleigh distribution

Description

Create UNU.RAN object for a Rayleigh distribution with scale parameter scale.

[Distribution] -- Rayleigh.

Usage

udrayleigh(scale=1, lb=0, ub=Inf)

Value

An object of class "unuran.cont".

Arguments

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

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 domain of the distribution can be truncated to the interval (lb,ub).

References

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

unuran.cont.

Examples

## Create distribution object for standard Rayleigh distribution
distr <- udrayleigh()
## Generate generator object; use method PINV (inversion)
gen <- pinvd.new(distr)
## Draw a sample of size 100
x <- ur(gen,100)