Parameter link functions for the $\mu$ and
$\lambda$ parameters.
See Links for more choices.
emu, elambda
List. Extra argument for each of the links.
See earg in Links for general information.
ilambda
Initial value for the $\lambda$ parameter.
zero
An integer-valued vector specifying which
linear/additive predictors $\eta_j$
are modelled as intercepts only.
The values must be from the set {1,2}.
Value
An object of class "vglmff" (see vglmff-class).
The object is used by modelling functions such as vglm,
rrvglm
and vgam.
pkg
SuppDists
Details
The inverse Gaussian distribution has a density
that can be written as
$$f(y;\mu,\lambda) = \sqrt{\lambda/(2\pi y^3)}
\exp\left(-\lambda (y-\mu)^2/(2 \mu^2 y)\right)$$
where $y>0$,
$\mu>0$, and
$\lambda>0$.
The mean of $Y$ is $\mu$ and its variance is
$\mu^3/\lambda$.
By default, $\eta_1=\log(\mu)$ and
$\eta_2=\log(\lambda)$.
References
Johnson, N. L. and Kotz, S. and Balakrishnan, N. (1994)
Continuous Univariate Distributions,
2nd edition, Volume 1, New York: Wiley.
Evans, M., Hastings, N. and Peacock, B. (2000)
Statistical Distributions,
New York: Wiley-Interscience, Third edition.