| waldff {VGAM} | R Documentation |
Wald Distribution Family Function
Description
Estimates the parameter of the standard Wald distribution by maximum likelihood estimation.
Usage
waldff(llambda = "loglink", ilambda = NULL)
Arguments
llambda, ilambda |
See |
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).
Value
An object of class "vglmff"
(see vglmff-class).
The object is used by modelling functions
such as vglm,
and vgam.
Note
The VGAM family function inv.gaussianff
estimates the location parameter \mu too.
Author(s)
T. W. Yee
References
Johnson, N. L. and Kotz, S. and Balakrishnan, N. (1994). Continuous Univariate Distributions, 2nd edition, Volume 1, New York: Wiley.
See Also
inv.gaussianff,
rinv.gaussian.
Examples
wdata <- data.frame(y = rinv.gaussian(1000, mu = 1, exp(1)))
wfit <- vglm(y ~ 1, waldff(ilambda = 0.2), wdata, trace = TRUE)
coef(wfit, matrix = TRUE)
Coef(wfit)
summary(wfit)