Runuran (version 0.40)

udhyperbolic: UNU.RAN object for Hyperbolic distribution

Description

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.

Usage

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

Value

An object of class "unuran.cont".

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.

Author

Josef Leydold and Wolfgang H\"ormann .

Details

The hyperbolic distribution with parameters \(\mu\),\(\alpha\),\(\beta\), and \(\delta\) has density proportional to $$ f(x) = \exp( -\alpha \sqrt(\delta^2 + (x - \mu)^2) + \beta*(x-\mu) ) $$ where \(\alpha>|\beta|\) and \(\delta>0\).

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

See Also

unuran.cont.

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)