Generalized Inverse Gaussian {rmutil}

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.

Author(s)

J.K. Lindsey

See Also

dinvgauss for the inverse Gaussian distribution.

Examples

dginvgauss(10, 3, 1, 1)
pginvgauss(10, 3, 1, 1)
qginvgauss(0.4, 3, 1, 1)
rginvgauss(10, 3, 1, 1)