Estimates the parameter of the standard Wald distribution
by maximum likelihood estimation.
Usage
waldff(llambda = "loglink", ilambda = NULL)
Value
An object of class "vglmff"
(see vglmff-class).
The object is used by modelling functions
such as vglm,
and vgam.
Arguments
llambda,ilambda
See CommonVGAMffArguments for information.
Author
T. W. Yee
Details
The standard Wald distribution is a special case of the
inverse Gaussian distribution with \(\mu=1\).
It has a density that can be written as
$$f(y;\lambda) = \sqrt{\lambda/(2\pi y^3)}
\; \exp\left(-\lambda (y-1)^2/(2 y)\right)$$
where \(y>0\) and \(\lambda>0\).
The mean of \(Y\) is \(1\)
(returned as the fitted values) and its variance is
\(1/\lambda\).
By default, \(\eta=\log(\lambda)\).
References
Johnson, N. L. and Kotz, S. and Balakrishnan, N. (1994).
Continuous Univariate Distributions,
2nd edition,
Volume 1,
New York: Wiley.