Runuran (version 0.30)

udmeixner: UNU.RAN object for Meixner distribution

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

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.

Value

An object of class "unuran.cont".

Details

The Mexiner distribution with parameters \(\alpha\), \(\beta\), \(\delta\), and \(\mu\) has density $$ f(x) = \kappa \,\exp(\beta(x-\mu)/\alpha) \, |\Gamma\left(\delta+ i(x-\mu)/\alpha\right)|^2 $$ where the normalization constant is given by $$ \kappa = \frac{\left(2\cos\left(\beta/2\right)\right)^{2\delta}}{ 2 \alpha \pi \, \Gamma\left(2 \delta\right)} $$

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).

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

# NOT RUN {
## 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)

# }