Hyperbolic Moments and Mode {HyperbolicDist} | 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)
Theta |
Parameter vector of the hyperbolic distribution. |
hyperbMean
gives the mean of the hyperbolic distribution,
hyperbVar
the variance, and hyperbMode
the mode.
The formulae used are as given in Barndorff-Nielsen and
Blęsild (1983), p. 702. hyperbSkew
and
hyperbKurt
are the skewness and kurtosis of the hyperbolic
distribution. The formulae used are those of Barndorff-Nielsen and
Blęsild (1981), Appendix 2. 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 parameterisation of the hyperbolic distribution used for this
and other components of the HyperbolicDist
package is the
(pi,zeta) one. See hyperbChangePars
to transfer between parameterisations.
David Scott d.scott@auckland.ac.nz, Richard Trendall, Thomas Tran
Barndorff-Nielsen, O. and Blęsild, 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 Blęsild, 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.
dhyperb
, hyperbChangePars
,
besselK
Theta <- c(2,2,2,2) hyperbMean(Theta) hyperbVar(Theta) hyperbSkew(Theta) hyperbKurt(Theta) hyperbMode(Theta)