# waldff: Wald Distribution Family Function In VGAM: Vector Generalized Linear and Additive Models

## Description

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

## Usage

 `1` ```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.

T. W. Yee

## References

Johnson, N. L. and Kotz, S. and Balakrishnan, N. (1994). Continuous Univariate Distributions, 2nd edition, Volume 1, New York: Wiley.

`inv.gaussianff`, `rinv.gaussian`.
 ```1 2 3 4 5``` ```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) ```