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 invgauss Inverse Gaussian Distribution
DESCRIPTION
Density, cumulative probability, quantiles and random generation for the inverse Gaussian distribution.

USAGE
dinvgauss(x, mu, lambda=1)
pinvgauss(q, mu, lambda=1)
qinvgauss(p, mu, lambda=1)
rinvgauss(n, mu, lambda=1)

REQUIRED 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.

OPTIONAL ARGUMENTS
 lambda vector of (positive) precision parameters. This is replicated to be the same length as p or q or the number of deviates generated. The variance of the distribution is mu3/lambda.

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.

SIDE EFFECTS
The function rinvgauss causes creation of the dataset .Random.seed if it does not already exist, otherwise its value is updated.

BACKGROUND
The inverse Gaussian distribution takes values on the positive real line. 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.

Giner, G, and Smyth, GK (2016). statmod: Probability Calculations for the Inverse Gaussian Distribution. [arXiv:1603.06687]

ACKNOWLEDGEMENT
The function qinvgauss was contributed by Dr Paul Bagshaw of the Centre National d'Etudes des Telecommunications (DIH/DIPS), France.