udhyperbolic function

UNU.RAN object for Hyperbolic distribution

Create UNU.RAN object for a Hyperbolic distribution with location parameter mu, tail (shape) parameter alpha, asymmetry (shape) parameter beta, and scale parameter delta.

[Distribution] -- Hyperbolic.

udhyperbolic(alpha, beta, delta, mu, lb=-Inf, ub=Inf)

Arguments

• alpha: tail (shape) parameter (must be strictly larger than absolute value of beta).
• beta: asymmetry (shape) parameter.
• delta: scale parameter (must be strictly positive).
• mu: location parameter.
• lb: lower bound of (truncated) distribution.
• ub: upper bound of (truncated) distribution.

Details

The hyperbolic distribution with parameters $mu$,$alpha$,$beta$, and $delta$

has density proportional to

where $alpha > |beta|$ and $delta>0$.

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

Returns

An object of class "unuran.cont".

See Also

unuran.cont.

Author(s)

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

Examples

## Create distribution object for hyperbolic distribution
distr <- udhyperbolic(alpha=3,beta=2,delta=1,mu=0)
## Generate generator object; use method PINV (inversion)
gen <- pinvd.new(distr)
## Draw a sample of size 100
x <- ur(gen,100)