udgig {Runuran}

UNU.RAN object for Generalized Inverse Gaussian distribution

Description

Create UNU.RAN object for a Generalized Inverse Gaussian distribution. Two parametrizations are available.

[Distribution] – Generalized Inverse Gaussian.

Usage

udgig(theta, psi, chi, lb=0, ub=Inf)
udgiga(theta, omega, eta=1, lb=0, ub=Inf)

Arguments

theta

shape parameter.

psi, chi

shape parameters (must be strictly positive).

omega, eta

shape parameters (must be strictly positive).

lb

lower bound of (truncated) distribution.

ub

upper bound of (truncated) distribution.

Details

The generalized inverse Gaussian distribution with parameters \theta, \psi, and \chi has density proportional to

f(x) = x^{\theta-1} \exp\left( -\frac{1}{2} \left(\psi x + \frac{\chi}{x}\right)\right)

where \psi>0 and \chi>0.

An alternative parametrization used parameters \theta, \omega, and \eta and has density proportional to

f(x) = x^{\theta-1} \exp\left( -\frac{\omega}{2} \left(\frac{x}{\eta}+\frac{\eta}{x}\right)\right)

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

Value

An object of class "unuran.cont".

Note

These two parametrizations can be converted into each other by means of the following transformations:

\psi = \frac{\omega}{\eta},\;\;\; \chi = \omega\eta

\omega = \sqrt{\chi\psi},\;\;\; \eta = \sqrt{\frac{\chi}{\psi}}

Author(s)

Josef Leydold and Wolfgang H\"ormann [e-mail].

References

N.L. Johnson, S. Kotz, and N. Balakrishnan (1994): Continuous Univariate Distributions, Volume 1. 2nd edition, John Wiley & Sons, Inc., New York. Chap. 15, p. 284.

See Also

unuran.cont.

Examples

## Create distribution object for GIG distribution
distr <- udgig(theta=3, psi=1, chi=1)
## Generate generator object; use method PINV (inversion)
gen <- pinvd.new(distr)
## Draw a sample of size 100
x <- ur(gen,100)