rmutil (version 1.1.4)

Generalized Inverse Gaussian: Generalized Inverse Gaussian Distribution

Description

These functions provide information about the generalized inverse Gaussian distribution with mean equal to m, dispersion equal to s, and family parameter equal to f: density, cumulative distribution, quantiles, log hazard, and random generation.

The generalized inverse Gaussian distribution has density $$ f(y) = \frac{y^{\nu-1}}{2 \mu^\nu K(1/(\sigma \mu),abs(\nu))} \exp(-(1/y+y/\mu^2)/(2*\sigma))$$ where \(\mu\) is the mean of the distribution, \(\sigma\) the dispersion, \(\nu\) is the family parameter, and \(K()\) is the fractional Bessel function of the third kind.

\(\nu=-1/2\) yields an inverse Gaussian distribution, \(\sigma=\infty\), \(\nu>0\) a gamma distribution, and \(\nu=0\) a hyperbola distribution.

Usage

dginvgauss(y, m, s, f, log=FALSE)
pginvgauss(q, m, s, f)
qginvgauss(p, m, s, f)
rginvgauss(n, m, s, f)

Arguments

y

vector of responses.

q

vector of quantiles.

p

vector of probabilities

n

number of values to generate

m

vector of means.

s

vector of dispersion parameters.

f

vector of family parameters.

log

if TRUE, log probabilities are supplied.

See Also

dinvgauss for the inverse Gaussian distribution.

Examples

# NOT RUN {
dginvgauss(10, 3, 1, 1)
pginvgauss(10, 3, 1, 1)
qginvgauss(0.4, 3, 1, 1)
rginvgauss(10, 3, 1, 1)
# }