udig() R function from [Runuran]

UNU.RAN object for Inverse Gaussian distribution

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

[Distribution] -- Inverse Gaussian (Wald).


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.

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} )f(x) = sqrt(lambda / (2*pi*x^3)) * exp( -(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).

Returns

An object of class "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. 259.

Author(s)

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

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)

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Maintainer: Josef Leydold
License: GPL (>= 2)
Last published: 2025-04-07

Useful links

udig function