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)
hginvgauss(y, 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 1.0

Index]