urcauchy {Runuran}

UNU.RAN Cauchy random variate generator

Description

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.

Usage

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

Arguments

n

size of required sample.

location

location parameter.

scale

(strictly positive) scale parameter.

lb

lower bound of (truncated) distribution.

ub

upper bound of (truncated) distribution.

Details

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).

Note

This function is wrapper for the UNU.RAN class in R. Compared to rcauchy, urcauchy is faster, especially for larger sample sizes. However, in opposition to rcauchy vector arguments are ignored, i.e. only the first entry is used.

Author(s)

Josef Leydold and Wolfgang H\"ormann [e-mail].

References

W. H\"ormann, J. Leydold, and G. Derflinger (2004): Automatic Nonuniform Random Variate Generation. Springer-Verlag, Berlin Heidelberg

See Also

runif and .Random.seed about random number generation, unuran for the UNU.RAN class, and rcauchy for the R built-in generator.

Examples

## Create a sample of size 1000
x <- urcauchy(n=1000)