|Specific Hyperbolic Distribution Moments and Mode||R Documentation|
Functions to calculate the mean, variance, skewness, kurtosis and mode of a specific hyperbolic distribution.
hyperbMean(Theta) hyperbVar(Theta) hyperbSkew(Theta) hyperbKurt(Theta) hyperbMode(Theta)
Parameter vector of the hyperbolic distribution.
The formulae used for the mean, variance and mode are as given in Barndorff-Nielsen and Bl<e6>sild (1983), p. 702. The formulae used for the skewness and kurtosis are those of Barndorff-Nielsen and Bl<e6>sild (1981), Appendix 2.
Note that the variance, skewness and kurtosis can be obtained from the
functions for the generalized hyperbolic distribution as special
cases. Likewise other moments can be obtained from the function
ghypMom which implements a recursive method to moments
of any desired order. Note that functions for the generalized
hyperbolic distribution use a different parameterization, so care is
hyperbMean gives the mean of the hyperbolic distribution,
hyperbVar the variance,
hyperbSkew the skewness,
hyperbKurt the kurtosis and
hyperbMode the mode.
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 of the hyperbolic distribution used for this
and other components of the
HyperbolicDist package is the
(pi,zeta) one. See
to transfer between parameterizations.
David Scott email@example.com, Richard Trendall, Thomas Tran
Barndorff-Nielsen, O. and Bl<e6>sild, P (1981). Hyperbolic distributions and ramifications: contributions to theory and application. In Statistical Distributions in Scientific Work, eds., Taillie, C., Patil, G. P., and Baldessari, B. A., Vol. 4, pp. 19–44. Dordrecht: Reidel.
Barndorff-Nielsen, O. and Bl<e6>sild, P (1983). Hyperbolic distributions. In Encyclopedia of Statistical Sciences, eds., Johnson, N. L., Kotz, S. and Read, C. B., Vol. 3, pp. 700–707. New York: Wiley.
Theta <- c(2,2,2,2) hyperbMean(Theta) hyperbVar(Theta) hyperbSkew(Theta) hyperbKurt(Theta) hyperbMode(Theta)
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