R: Wald Distribution Family Function

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 `CommonVGAMffArguments` for information.

### 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`, `rinv.gaussian`.

### Examples

    wdata <- data.frame(y = rinv.gaussian(n = 1000, mu =  1, lambda = exp(1)))
    wfit <- vglm(y ~ 1, waldff(ilambda = 0.2), data = wdata, trace = TRUE)
    coef(wfit, matrix = TRUE)
    Coef(wfit)
    summary(wfit)

[Package VGAM version 1.1-3 Index]