UNU.RAN object for Meixner distribution

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Description

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

[Distribution] – Meixner.

Usage

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

Arguments

alpha

scale parameter (must be strictly positive).

beta

asymmetry (shape) parameter (must be larger than -pi and smaller than pi).

delta

shape parameter (must be strictly positive).

mu

location parameter.

lb

lower bound of (truncated) distribution.

ub

upper bound of (truncated) distribution.

Details

The Mexiner distribution with parameters alpha, beta, delta, and mu has density

f(x) = kappa * exp(beta*(x-mu)/alpha) * |Gamma(delta + i * (x-mu)/alpha)|^2

where the normalization constant is given by

kappa = (2*cos(beta/2))^(2*delta) / (2 * alpha * pi * Gamma(2*delta))

The symbol i denotes the imaginary unit, that is, we have to evaluate the gamma function Gamma(z) for complex arguments z = x + i*y.

Notice that alpha>0, |beta| < pi 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 Kemal Dingec unuran@statmath.wu.ac.at.

References

Grigelionis, B., 1999. Processes of Meixner type. Lithuanian Mathematical Journal, Vol. 39, p. 33–41.

Schoutens, W., 2001. The Meixner Processes in Finance. Eurandom Report 2001-002, Eurandom, Eindhoven.

See Also

unuran.cont.

Examples

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## Create distribution object for meixner distribution
distr <- udmeixner(alpha=0.0298, beta=0.1271, delta=0.5729, mu=-0.0011)
## 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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