Inverse Gaussian Distribution
Density, cumulative probability, quantiles and random generation for the inverse Gaussian distribution.
dinvgauss(x, mean=1, shape=NULL, dispersion=1, log=FALSE) pinvgauss(q, mean=1, shape=NULL, dispersion=1, lower.tail=TRUE, log.p=FALSE) qinvgauss(p, mean=1, shape=NULL, dispersion=1, lower.tail=TRUE, log.p=FALSE, maxit=50L, tol=1e-5, trace=FALSE) rinvgauss(n, mean=1, shape=NULL, dispersion=1)
- vector of quantiles.
- vector of probabilities.
- sample size. If
length(n)is larger than 1, then
length(n)random values are returned.
- vector of (positive) means.
- vector of (positive) shape parameters.
- vector of (positive) dispersion parameters.
- logical; if
TRUE, probabilities are P(X
- logical; if
TRUE, the log-density is returned.
- logical; if
TRUE, probabilities are on the log-scale.
- maximum number of Newton iterations used to find
- small positive numeric value giving the convergence tolerance for the quantile.
- logical, if
TRUEthen the working estimate for
qfrom each iteration will be output.
The inverse Gaussian distribution takes values on the positive real line (Tweedie, 1957; Chhikara and Folks, 1989).
It is somewhat more right skew than the gamma distribution, with variance given by
The shape and dispersion parameters are alternative parametrizations for the variability, the shape being the inverse of the dispersion.
The distribution has applications in reliability and survival analysis, and is one of the response distributions used in generalized linear models.
pinvgauss uses a result from Chhikara and Folks (1974), with enhancements for right tails and log-probabilities.
rinvgauss uses an algorithm from Michael et al (1976).
qinvgauss uses code and algorithm from Giner and Smyth (2014).
- Output values give density (
dinvgauss), probability (
pinvgauss), quantile (
qinvgauss) or random sample (
rinvgauss) for the inverse Gaussian distribution with mean
dispersion. Output is a vector of length equal to the maximum length of any of the arguments
dispersion. If the first argument is the longest, then all the attributes of the input argument are preserved on output, for example, a matrix
xwill give a matrix on output. Elements of
pthat are missing will cause the corresponding elements of the result to be missing, as will non-positive values for
Chhikara, R. S., and Folks, J. L., (1989).
The inverse Gaussian distribution: Theory, methodology and applications.
Marcel Dekker, New York.
Chhikara, R. S., and Folks, J. L., (1974).
Estimation of the inverse Gaussian distribution function.
Journal of the American Statistical Association 69, 250-254.
Giner, G., and Smyth, G. K. (2014).
A monotonically convergent Newton iteration for the quantiles of any unimodal distribution, with application to the inverse Gaussian distribution.
rinvGauss in the SuppDists package.
q <- rinvgauss(20,mean=1,dispersion=0.5) # generate vector of 20 random numbers p <- pinvgauss(q,mean=1,dispersion=0.5) # p should be uniform