statmod (version 1.4.19)

invgauss: Inverse Gaussian Distribution

Description

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

Usage

dinvgauss(x, mu, lambda=1, log=FALSE)
pinvgauss(q, mu, lambda=1)
qinvgauss(p, mu, lambda=1, iter=20L, trace=FALSE)
rinvgauss(n, mu, lambda=1)

Arguments

x

vector of quantiles. Missing values (NAs) are allowed.

q

vector of quantiles. Missing values (NAs) are allowed.

p

vector of probabilities. Missing values (NAs) are allowed.

n

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

mu

vector of (positive) means. This is replicated to be the same length as p or q or the number of deviates generated.

lambda

vector of (positive) precision parameters. This is replicated to be the same length as p or q or the number of deviates generated.

log

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

iter

number of Newton iterations used to find q from p.

trace

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

Value

• Vector of same length as x or q giving the density (dinvgauss), probability (pinvgauss), quantile (qinvgauss) or random sample (rinvgauss) for the inverse Gaussian distribution with mean mu and inverse dispersion lambda. Elements of q or p that are missing will cause the corresponding elements of the result to be missing.

Details

The inverse Gaussian distribution takes values on the positive real line. The variance of the distribution is $\mu^3/\lambda$. Applications of the inverse Gaussian include sequential analysis, diffusion processes and radiotechniques. The inverse Gaussian is one of the response distributions used in generalized linear models.

References

Chhikara, R. S., and Folks, J. Leroy, (1989). The inverse Gaussian distribution: Theory, methodology, and applications. Marcel Dekker, New York.

See Also

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

Examples

y <- rinvgauss(20,1,2) # generate vector of 20 random numbers
p <- pinvgauss(y,1,2) # p should be uniform