udcauchy function

UNU.RAN object for Cauchy distribution

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

[Distribution] -- Cauchy.

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.

Details

The Cauchy distribution with location $l$ and scale $s$ has density

for all $x$.

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

Returns

An object of class "unuran.cont".

See Also

unuran.cont.

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.

Author(s)

Josef Leydold and Wolfgang H"ormann unuran@statmath.wu.ac.at .

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)