udgig | R Documentation |
Create UNU.RAN object for a Generalized Inverse Gaussian distribution. Two parametrizations are available.
[Distribution] – Generalized Inverse Gaussian.
udgig(theta, psi, chi, lb=0, ub=Inf) udgiga(theta, omega, eta=1, lb=0, ub=Inf)
theta |
shape parameter. |
psi, chi |
shape parameters (must be strictly positive). |
omega, eta |
shape parameters (must be strictly positive). |
lb |
lower bound of (truncated) distribution. |
ub |
upper bound of (truncated) distribution. |
The generalized inverse Gaussian distribution with parameters theta, psi, and chi has density proportional to
f(x) = x^(theta-1) * exp( -1/2 * (psi*x + chi/x) )
where psi>0 and chi>0.
An alternative parametrization used parameters theta, omega, and eta and has density proportional to
f(x) = x^(theta-1) * exp( -omega/2 * (x/eta + eta/x) )
The domain of the distribution can be truncated to the
interval (lb
,ub
).
An object of class "unuran.cont"
.
These two parametrizations can be converted into each other by means of the following transformations:
psi = omega/eta, chi = omega*eta
omega = sqrt(chi*psi), eta = sqrt(chi/psi)
Josef Leydold and Wolfgang H\"ormann unuran@statmath.wu.ac.at.
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.
unuran.cont
.
## Create distribution object for GIG distribution distr <- udgig(theta=3, psi=1, chi=1) ## 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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