Runuran (version 0.40)

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)

Value

An object of class "unuran.cont".

Arguments

mu

mean (strictly positive).

lambda

shape parameter (strictly positive).

lb

lower bound of (truncated) distribution.

ub

upper bound of (truncated) distribution.

Author

Josef Leydold and Wolfgang H\"ormann .

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)