# udmeixner: UNU.RAN object for Meixner distribution In Runuran: R Interface to the UNU.RAN Random Variate Generators

## 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

 `1` ```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 [email protected].

## 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.

`unuran.cont`.
 ```1 2 3 4 5 6``` ```## 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) ```