The Inverse Gaussian Distribution

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.

Value

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

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.

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.

Note

Currently qinv.gaussian is unavailable.

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")
#> Error in h(simpleError(msg, call)): error in evaluating the argument 'x' in selecting a method for function 'plot': object 'x' not found
abline(h = 0, col = "gray", lty = 2)
#> Error in int_abline(a = a, b = b, h = h, v = v, untf = untf, ...): plot.new has not been called yet
lines(x, pinv.gaussian(x, mu = 1, lambda = 1), type = "l", col = "orange")  # \dontrun{}
#> Error: object 'x' not found