UNU.RAN random variate generator for the Generalized Inverse Gaussian
Distribution with parameters lambda and omega.
It also allows sampling from the truncated distribution.
[Special Generator] -- Sampling Function: GIG (generalized inverse Gaussian).
urgig(n, lambda, omega, lb=1.e-12, ub=Inf)
size of required sample.
(strictly positive) shape parameter.
(strictly positive) shape parameter.
lower bound of (truncated) distribution
upper bound of (truncated) distribution
Josef Leydold and Wolfgang H\"ormann unuran@statmath.wu.ac.at.
The Generalized Inverse Gaussian distribution with parameters
lambda \(=\lambda\) and omega \(=\omega\)
has a density proportional to
$$
f(x) \sim x^{\lambda-1}\exp(-(\omega/2)(x+1/x))
$$
for \(x \ge 0\), \(\lambda > 0\) and \(\omega > 0\).
The generation algorithm uses transformed density rejection ‘TDR’. The
parameters lb and ub can be used to generate variates from
the distribution truncated to the interval (lb,ub).
The generation algorithm works for \(\lambda \ge 1\) and \(\omega>0\) and for \(\lambda>0\) and \(\omega \ge 0.5\).
W. H\"ormann, J. Leydold, and G. Derflinger (2004): Automatic Nonuniform Random Variate Generation. Springer-Verlag, Berlin Heidelberg.
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.
runif and .Random.seed about random number
generation and unuran for the UNU.RAN class.
## Create a sample of size 1000
x <- urgig(n=1000,lambda=2,omega=3)
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