Generalized Inverse Gaussian Moments and Mode {HyperbolicDist} | R Documentation |
Functions to calculate the mean, variance, skewness, kurtosis and mode of a specific generalized inverse Gaussian distribution.
gigMean(Theta) gigVar(Theta) gigSkew(Theta) gigKurt(Theta) gigMode(Theta)
Theta |
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 J{o}rgensen (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
J{o}rgensen, B. (1982). Statistical Properties of the Generalized Inverse Gaussian Distribution. Lecture Notes in Statistics, Vol. 9, Springer-Verlag, New York.
Theta <- c(-0.5,5,2.5) gigMean(Theta) gigVar(Theta) gigSkew(Theta) gigKurt(Theta) gigMode(Theta)