# GInvGauss: Generalized Inverse Gaussian Distribution In rmutil: Utilities for Nonlinear Regression and Repeated Measurements Models

 Generalized Inverse Gaussian 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

`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)
```

rmutil documentation built on March 18, 2022, 6:55 p.m.