invgauss {statmod} | R Documentation |

## Inverse Gaussian Distribution

### Description

Density, cumulative probability, quantiles and random generation for the inverse Gaussian 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 $μ^3/λ$. 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.

### Author(s)

Gordon Smyth; Paul Bagshaw, Centre National d'Etudes des Telecommunications (DIH/DIPS), France (`qinvgauss`

); Trevor Park,
Department of Statistics, University of Florida

### 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

[Package

*statmod* version 1.2.4

Index]