udgig function

UNU.RAN object for Generalized Inverse Gaussian distribution

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

[Distribution] -- Generalized Inverse Gaussian.

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

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

where $psi>0$ and $chi>0$.

An alternative parametrization used parameters $theta$, $omega$, and $eta$

and has density proportional to

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

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

Returns

An object of class "unuran.cont".

Note

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

$$\psi = \frac{\omega}{\eta},\;\;\;\chi = \omega\etapsi = omega/eta, chi = omega*eta$$ $$\omega = \sqrt{\chi\psi},\;\;\;\eta = \sqrt{\frac{\chi}{\psi}}omega = sqrt(chi*psi), eta = sqrt(chi/psi)$$

See Also

unuran.cont.

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.

Author(s)

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

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)