# invgauss

From statmod v1.2.0
by Gordon Smyth

##### Inverse Gaussian Distribution

Density, cumulative probability, quantiles and random generation for the inverse Gaussian distribution.

- Keywords
- distribution

##### Usage

```
dinvgauss(x, mu, lambda=1)
pinvgauss(q, mu, lambda=1)
qinvgauss(p, mu, lambda=1)
rinvgauss(n, mu, lambda=1)
```

##### Arguments

- x
- vector of quantiles. Missing values (NAs) are allowed.
- q
- vector of quantiles. Missing values (NAs) are allowed.
- p
- vector of probabilities. Missing values (NAs) are allowed.
- n
- sample size. If
`length(n)`

is larger than 1, then`length(n)`

random values are returned. - mu
- vector of (positive) means. This is replicated to be the same length as
`p`

or`q`

or the number of deviates generated. - lambda
- vector of (positive) precision parameters. This is replicated to be the same length as
`p`

or`q`

or the number of deviates generated.

##### Details

The inverse Gaussian distribution takes values on the positive real line. The variance of the distribution is $\mu^3/\lambda$. Applications of the inverse Gaussian include sequential analysis, diffusion processes and radiotechniques. The inverse Gaussian is one of the response distributions used in generalized linear models.

##### Value

- Vector of same length as
`x`

or`q`

giving the density (`dinvgauss`

), probability (`pinvgauss`

), quantile (`qinvgauss`

) or random sample (`rinvgauss`

) for the inverse Gaussian distribution with mean`mu`

and inverse dispersion`lambda`

. Elements of`q`

or`p`

that are missing will cause the corresponding elements of the result to be missing.

##### References

Chhikara, R. S., and Folks, J. Leroy, (1989). *The inverse Gaussian distribution: Theory, methodology, and applications*. Marcel Dekker, New York.

##### See Also

`dinvGauss`

, `pinvGauss`

, `qinvGauss`

and `rinvGauss`

in the SuppDists package.

##### Examples

```
y <- rinvgauss(20,1,2) # generate vector of 20 random numbers
p <- pinvgauss(y,1,2) # p should be uniform
```

*Documentation reproduced from package statmod, version 1.2.0, License: LGPL version 2 or newer*

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