inv.gaussianff {VGAM} | R Documentation

## Inverse Gaussian Distribution Family Function

### Description

Estimates the two parameters of the inverse Gaussian distribution by maximum likelihood estimation.

### Usage

    inv.gaussianff(lmu="loge", llambda="loge",
                   emu=list(), elambda=list(),
                   ilambda=1, zero=NULL)

### Arguments

`lmu, llambda` | Parameter link functions for the mu and lambda parameters. See `Links` for more choices.
`emu, elambda` | List. Extra argument for each of the links. See `earg` in `Links` for general information.
`ilambda` | Initial value for the lambda parameter.
`zero` | An integer-valued vector specifying which linear/additive predictors eta_j are modelled as intercepts only. The values must be from the set {1,2}.

### Details

The inverse Gaussian distribution has a density that can be written as

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

where y>0, mu>0, and lambda>0. The mean of Y is mu and its variance is mu^3/lambda. By default, eta1=log(mu) and eta2=log(lambda).

### Value

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

### Note

The inverse Gaussian distribution can be fitted (to a certain extent) using the usual GLM framework involving a scale parameter. This family function is different from that approach in that it estimates both parameters by full maximum likelihood estimation.

### 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.

Evans, M., Hastings, N. and Peacock, B. (2000) Statistical Distributions, New York: Wiley-Interscience, Third edition.

### See Also

`Inv.gaussian`, `wald`, `bisa`.

The R{} package SuppDists has several functions for evaluating the density, distribution function, quantile function and generating random numbers from the inverse Gaussian distribution.

### Examples

    n = 1000
    shape = exp(3)
    y = rinv.gaussian(n=n, mu=exp(2), lambda=shape)
    fit = vglm(y ~ 1, inv.gaussianff(ilam=shape), trace=TRUE)
    coef(fit, matrix=TRUE)
    Coef(fit)
    summary(fit)

[Package VGAM version 0.7-9 Index]