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 = "loglink", llambda = "loglink",
                   imethod = 1, ilambda = NULL,
                   parallel = FALSE, ishrinkage = 0.99, zero = NULL)

### Arguments

`lmu, llambda` | Parameter link functions for the mu and lambda parameters. See `Links` for more choices.
`ilambda, parallel` | See `CommonVGAMffArguments` for more information. If `parallel = TRUE` then the constraint is not applied to the intercept.
`imethod, ishrinkage, zero` | See `CommonVGAMffArguments` for information.

### Details

The standard (“canonical”) form of 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). The mean is returned as the fitted values. This VGAM family function can handle multiple responses (inputted as a matrix).

### 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.

Forbes, C., Evans, M., Hastings, N. and Peacock, B. (2011) Statistical Distributions, Hoboken, NJ, USA: John Wiley and Sons, Fourth edition.

### See Also

`Inv.gaussian`, `waldff`, `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

    idata <- data.frame(x2 = runif(nn <- 1000))
    idata <- transform(idata, mymu   = exp(2 + 1 * x2),
                              Lambda = exp(2 + 1 * x2))
    idata <- transform(idata, y = rinv.gaussian(nn, mu = mymu, lambda = Lambda))
    fit1 <-   vglm(y ~ x2, inv.gaussianff, data = idata, trace = TRUE)
    rrig <- rrvglm(y ~ x2, inv.gaussianff, data = idata, trace = TRUE)
    coef(fit1, matrix = TRUE)
    coef(rrig, matrix = TRUE)
    Coef(rrig)
    summary(fit1)

[Package VGAM version 1.1-1 Index]