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 0.7-9 Index]