VGAM (version 0.9-2)

waldff: Wald Distribution Family Function

Description

Estimates the parameter of the standard Wald distribution by maximum likelihood estimation.

Usage

waldff(link.lambda = "loge", init.lambda = NULL)

Arguments

link.lambda

Parameter link function for the $\lambda$ parameter. See Links for more choices and general information.

init.lambda

Initial value for the $\lambda$ parameter. The default means an initial value is chosen internally.

Value

• An object of class "vglmff" (see vglmff-class). The object is used by modelling functions such as vglm, and vgam.

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 $$f(y;\lambda )=\sqrt{\lambda /(2\pi y^3)}\exp (-\lambda (y-1{)}^2/(2y))$$ 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(n = 1000, mu =  1, lambda = exp(1)))
fit <- vglm(y ~ 1, waldff(init = 0.2), wdata, trace = TRUE)
coef(fit, matrix = TRUE)
Coef(fit)
summary(fit)