Runuran (version 0.21.0)

udig: UNU.RAN object for Inverse Gaussian distribution

Description

Create UNU.RAN object for a Inverse Gaussian (Wald) distribution with mean mu and shape parameter lambda. [Distribution] -- Inverse Gaussian (Wald).

Usage

udig(mu, lambda, lb=0, ub=Inf)

Arguments

mu

mean (strictly positive).

lambda

shape parameter (strictly positive).

lb

lower bound of (truncated) distribution.

ub

upper bound of (truncated) distribution.

Value

• An object of class "unuran.cont".

Details

The inverse Gaussian distribution with mean $\mu$ and shape parameter $\lambda$ has density $$f(x) = \sqrt{\frac{\lambda}{2 \pi x^3} } \exp( -\frac{\lambda (x-\mu)^2}{2\mu^2 x} )$$ where $\mu>0$ and $\lambda>0$.

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

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. 259.

See Also

unuran.cont.

Examples

## Create distribution object for inverse Gaussian distribution
distr <- udig(mu=3, lambda=2)
## Generate generator object; use method PINV (inversion)
gen <- pinvd.new(distr)
## Draw a sample of size 100
x <- ur(gen,100)