Runuran (version 0.21.0)

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)

Arguments

location

location parameter.

scale

(strictly positive) scale parameter.

lb

lower bound of (truncated) distribution.

ub

upper bound of (truncated) distribution.

Value

• An object of class "unuran.cont".

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)