VGAM (version 1.1-12)

Inv.gaussian: 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)

Value

dinv.gaussian gives the density,

pinv.gaussian gives the distribution function, and

rinv.gaussian generates random deviates.

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.

Author

T. W. Yee

Details

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

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

if (FALSE)  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")