UNU.RAN object for Hyperbolic distribution

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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

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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

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).

Value

An object of class "unuran.cont".

Author(s)

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

See Also

unuran.cont.

Examples

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## 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)

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