GeneralizedHyperbolic (version 0.8-6)

Specific Generalized Inverse Gaussian Moments and Mode: Moments and Mode of the Generalized Inverse Gaussian Distribution

Description

Functions to calculate the mean, variance, skewness, kurtosis and mode of a specific generalized inverse Gaussian distribution.

Usage

gigMean(chi = 1, psi = 1, lambda = 1,
        param = c(chi, psi, lambda))
gigVar(chi = 1, psi = 1, lambda = 1,
       param = c(chi, psi, lambda))
gigSkew(chi = 1, psi = 1, lambda = 1,
        param = c(chi, psi, lambda))
gigKurt(chi = 1, psi = 1, lambda = 1,
        param = c(chi, psi, lambda))
gigMode(chi = 1, psi = 1, lambda = 1,
        param = c(chi, psi, lambda))

Value

gigMean gives the mean of the generalized inverse Gaussian distribution, gigVar the variance, gigSkew the skewness,

gigKurt the kurtosis, and gigMode the mode. The formulae used are as given in Jorgensen (1982), pp. 13--17. Note that the kurtosis is the standardised fourth cumulant or what is sometimes called the kurtosis excess. (See

http://mathworld.wolfram.com/Kurtosis.html for a discussion.)

The parameterization used for the generalized inverse Gaussian distribution is the \((\chi, \psi)\) one (see

dgig). To use another parameterization, use

gigChangePars.

Arguments

chi

A shape parameter that by default holds a value of 1.

psi

Another shape parameter that is set to 1 by default.

lambda

Shape parameter of the GIG distribution. Common to all forms of parameterization. By default this is set to 1.

param

Parameter vector of the generalized inverse Gaussian distribution.

Author

David Scott

References

Jorgensen, B. (1982). Statistical Properties of the Generalized Inverse Gaussian Distribution. Lecture Notes in Statistics, Vol. 9, Springer-Verlag, New York.

See Also

dgig, gigChangePars, besselK

Examples

param <- c(5, 2.5, -0.5)
gigMean(param = param)
gigVar(param = param)
gigSkew(param = param)
gigKurt(param = param)
gigMode(param = param)