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.

`dinvGauss`, `pinvGauss`, `qinvGauss` and `rinvGauss` in the SuppDists package.
```y <- rinvgauss(20,1,2) # generate vector of 20 random numbers