Moments and Mode of the Generalized Inverse Gaussian Distribution
Functions to calculate the mean, variance, skewness, kurtosis and mode of a specific generalized inverse Gaussian distribution.
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))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. |
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.
David Scott d.scott@auckland.ac.nz
Jorgensen, B. (1982). Statistical Properties of the Generalized Inverse Gaussian Distribution. Lecture Notes in Statistics, Vol. 9, Springer-Verlag, New York.
param <- c(5, 2.5, -0.5) gigMean(param = param) gigVar(param = param) gigSkew(param = param) gigKurt(param = param) gigMode(param = param)
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