udig {Runuran} | R Documentation |
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. |
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
).
Value
An object of class "unuran.cont"
.
Author(s)
Josef Leydold and Wolfgang H\"ormann unuran@statmath.wu.ac.at.
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
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)