UNU.RAN random variate generator for the Cauchy distribution with
location parameter location and scale parameter scale.
It also allows sampling from the truncated distribution.
[Special Generator] -- Sampling Function: Cauchy.
urcauchy(n, location=0, scale=1, lb = -Inf, ub = Inf)
size of required sample.
location parameter.
(strictly positive) scale parameter.
lower bound of (truncated) distribution.
upper bound of (truncated) distribution.
Josef Leydold and Wolfgang H\"ormann unuran@statmath.wu.ac.at.
If location or scale are not specified, they assume
the default values of 0 and 1 respectively.
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 generation algorithm uses fast numerical inversion. The parameters
lb and ub can be used to generate variates from
the Cauchy distribution truncated to the interval (lb,ub).
W. H\"ormann, J. Leydold, and G. Derflinger (2004): Automatic Nonuniform Random Variate Generation. Springer-Verlag, Berlin Heidelberg
runif and .Random.seed about random number
generation, unuran for the UNU.RAN class, and
rcauchy for the R built-in generator.
## Create a sample of size 1000
x <- urcauchy(n=1000)
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