VGAM (version 1.1-8)

waldff: Wald Distribution Family Function

Description

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.

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)