urhyperbolic function

UNU.RAN Hyperbolic random variate generator

UNU.RAN random variate generator for the Hyperbolic distribution with parameters shape and scale. It also allows sampling from the truncated distribution.

[Special Generator] -- Sampling Function: Hyperbolic.

urhyperbolic(n, shape, scale=1, lb = -Inf, ub = Inf)

Arguments

• n: size of required sample.
• shape: (strictly positive) shape parameter.
• scale: (strictly positive) scale parameter.
• lb: lower bound of (truncated) distribution.
• ub: upper bound of (truncated) distribution.

Details

If scale is omitted, it assumes the default value of 1.

The Hyperbolic distribution with parameters shape $= a$

and scale $= s$ has density proportional to

for all $x$, $a > 0$ and $s > 0$.

The generation algorithm uses transformed density rejection TDR . The parameters lb and ub can be used to generate variates from the Hyperbolic distribution truncated to the interval (lb,ub).

See Also

runif and .Random.seed about random number generation and unuran for the UNU.RAN class.

References

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

Author(s)

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

Note

This function is wrapper for the UNU.RAN class in .

Do not confuse with rhyper

that samples from the (discrete) hypergeometric distribution.

Examples

## Create a sample of size 1000 from Hyperbolic distribution with shape=3
x <- urhyperbolic(n=1000,shape=3)