Runuran (version 0.40)

udcauchy: UNU.RAN object for Cauchy distribution

Description

Create UNU.RAN object for a Cauchy distribution with location parameter location and scale parameter scale.

[Distribution] -- Cauchy.

Usage

udcauchy(location=0, scale=1, lb=-Inf, ub=Inf)

Value

An object of class "unuran.cont".

Arguments

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

The Cauchy distribution with location \(l\) and scale \(s\) has density $$f(x) = \frac{1}{\pi s} \left( 1 + \left(\frac{x - l}{s}\right)^2 \right)^{-1} $$ for all \(x\).

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. 16, p. 299.

See Also

unuran.cont.

Examples

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