R: Generalized Inverse Gaussian Distribution

Generalized Inverse Gaussian {rmutil} | R Documentation

## Generalized Inverse Gaussian Distribution

### Description

These functions provide information about the generalized inverse Gaussian distribution with mean equal to `m`, dispersion equal to `s`, and family parameter equal to `f`: density, cumulative distribution, quantiles, log hazard, and random generation.

The generalized inverse Gaussian distribution has density

f(y) = y^(f-1)/(2 m^f K(1/(s m),abs(f))) exp(-(1/y+y/m^2)/(2*s))

where m is the mean of the distribution, s the dispersion, f is the family parameter, and K() is the fractional Bessel function of the third kind.

f=-1/2 yields an inverse Gaussian distribution, s=infinity, f>0 a gamma distribution, and f=0 a hyperbola distribution.

### Usage

    dginvgauss(y, m, s, f, log=FALSE)
    pginvgauss(q, m, s, f)
    qginvgauss(p, m, s, f)
    rginvgauss(n, m, s, f)

### Arguments

`y` | vector of responses.
`q` | vector of quantiles.
`p` | vector of probabilities
`n` | number of values to generate
`m` | vector of means.
`s` | vector of dispersion parameters.
`f` | vector of family parameters.
`log` | if TRUE, log probabilities are supplied.

### Author(s)

J.K. Lindsey

### See Also

`dinvgauss` for the inverse Gaussian distribution.

### Examples

    dginvgauss(10, 3, 1, 1)
    pginvgauss(10, 3, 1, 1)
    qginvgauss(0.4, 3, 1, 1)
    rginvgauss(10, 3, 1, 1)

[Package rmutil version 1.1.3 Index]