statmod (version 1.4.23)

invgauss: Inverse Gaussian Distribution

Description

Density, cumulative probability, quantiles and random generation for the inverse Gaussian distribution.

Usage

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=200L, tol=1e-15, trace=FALSE)
rinvgauss(n, mean=1, shape=NULL, dispersion=1)

Arguments

x,q

vector of quantiles.

p

vector of probabilities.

n

sample size. If length(n) is larger than 1, then length(n) random values are returned.

mean

vector of (positive) means.

shape

vector of (positive) shape parameters.

dispersion

vector of (positive) dispersion parameters. Ignored if shape is not NULL, in which case dispersion=1/shape.

lower.tail

logical; if TRUE, probabilities are P(Xq).

log

logical; if TRUE, the log-density is returned.

log.p

logical; if TRUE, probabilities are on the log-scale.

maxit

maximum number of Newton iterations used to find q.

tol

small positive numeric value giving the convergence tolerance for the quantile.

trace

logical, if TRUE then the working estimate for q from each iteration will be output.

Value

• Output values give density (dinvgauss), probability (pinvgauss), quantile (qinvgauss) or random sample (rinvgauss) for the inverse Gaussian distribution with mean mean and dispersion dispersion. Output is a vector of length equal to the maximum length of any of the arguments x, q, mean, shape or dispersion. If the first argument is the longest, then all the attributes of the input argument are preserved on output, for example, a matrix x will give a matrix on output. Elements of input vectors that are missing will cause the corresponding elements of the result to be missing, as will non-positive values for mean or dispersion.

Details

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 dispersion*mean^3. The distribution has applications in reliability and survival analysis, and is one of the response distributions used in generalized linear models. The shape and dispersion parameters are alternative parametrizations for the variability, with dispersion=1/shape. Only one of these two arguments needs to be specified. If both are set, then shape takes precedence. 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).

References

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. http://www.statsci.org/smyth/pubs/qinvgaussPreprint.pdf Michael, J. R., Schucany, W. R., and Haas, R. W. (1976). Generating random variates using transformations with multiple roots. The American Statistician, 30, 88--90. Tweedie, M. C. (1957). Statistical Properties of Inverse Gaussian Distributions I. Annals of Mathematical Statistics 28, 362-377.

See Also

dinvGauss, pinvGauss, qinvGauss and rinvGauss in the SuppDists package.

Examples

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