urhyperbolic: UNU.RAN Hyperbolic random variate generator

In Runuran: R Interface to the 'UNU.RAN' Random Variate Generators

UNU.RAN Hyperbolic random variate generator

Description

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.

Usage

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 =\alpha and scale =\sigma has density proportional to

f(x) \sim \exp(-\alpha \sqrt{1+(\frac{x}{s})^2})

for all x, \alpha > 0 and \sigma > 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).

Note

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

Do not confuse with rhyper that samples from the (discrete) hypergeometric distribution.

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 and unuran for the UNU.RAN class.

Examples

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

Runuran documentation built on April 12, 2025, 1:35 a.m.