R: The Inverse Gaussian Distribution

Inv.gaussian {VGAM} | R Documentation

## The Inverse Gaussian Distribution

### Description

Density, distribution function and random generation for the inverse Gaussian distribution.

### Usage

    dinv.gaussian(x, mu, lambda, log = FALSE)
    pinv.gaussian(q, mu, lambda)
    rinv.gaussian(n, mu, lambda)

### Arguments

`x, q` | vector of quantiles.

`n` | number of observations. If `length(n) > 1` then the length is taken to be the number required.
`mu` | the mean parameter.
`lambda` | the lambda parameter.
`log` | Logical. If `log = TRUE` then the logarithm of the density is returned.

### Details

See `inv.gaussianff`, the VGAM family function for estimating both parameters by maximum likelihood estimation, for the formula of the probability density function.

### Value

`dinv.gaussian` gives the density, `pinv.gaussian` gives the distribution function, and `rinv.gaussian` generates random deviates.

### Note

Currently `qinv.gaussian` is unavailable.

### Author(s)

T. W. Yee

### References

Johnson, N. L. and Kotz, S. and Balakrishnan, N. (1994). Continuous Univariate Distributions, 2nd edition, Volume 1, New York: Wiley.

Taraldsen, G. and Lindqvist, B. H. (2005). The multiple roots simulation algorithm, the inverse Gaussian distribution, and the sufficient conditional Monte Carlo method. Preprint Statistics No. 4/2005, Norwegian University of Science and Technology, Trondheim, Norway.

### See Also

`inv.gaussianff`, `waldff`.

### Examples

    ## Not run:  x <- seq(-0.05, 4, len = 300)
    plot(x, dinv.gaussian(x, mu = 1, lambda = 1), type = "l",
         col = "blue",las = 1, main =
         "blue is density, orange is cumulative distribution function")
    abline(h = 0, col = "gray", lty = 2)
    lines(x, pinv.gaussian(x, mu = 1, lambda = 1), type = "l", col = "orange")
    ## End(Not run)

[Package VGAM version 1.1-3 Index]