wald {VGAM}R Documentation

Wald Distribution Family Function

Description

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

Usage

wald(link.lambda="loge", earg=list(), init.lambda=NULL)

Arguments

link.lambda Parameter link function for the lambda parameter. See Links for more choices.
earg List. Extra argument for the link. See earg in Links for general information.
init.lambda Initial value for the lambda parameter. The default means an initial value is chosen internally.

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;mu,lambda) = sqrt(lambda/(2*pi*y^3)) * exp(-lambda*(y-1)^2/(2*y))

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.

Examples

set.seed(123)
shape = 1
y = rgamma(n=1000, shape=shape) # Not inverse Gaussian!!
fit = vglm(y ~ 1, wald(init=0.2), trace=TRUE)
coef(fit, matrix=TRUE)
Coef(fit)
summary(fit)

[Package VGAM version 0.7-7 Index]