Functions used to calculate the mean, variance, skewness and kurtosis of a hyperbolic distribution. Not expected to be called directly by users.
1 2 3 4 5 6 7 8 9
Value of the parameter pi of the hyperbolic distribution.
Value of the parameter zeta of the hyperbolic distribution.
Parameter related to order of Bessel functions.
are used in the calculation of the mean and variance. They are
functions of the Bessel functions of the third kind,
implemented in R as
besselK. The other functions are
used in calculation of higher moments. See Barndorff-Nielsen, O. and
Blaesild, P (1981) for details of the calculations.
The parameterisation of the hyperbolic distribution used for this
and other components of the
HyperbolicDist package is the
(pi,zeta) one. See
transfer between parameterizations.
David Scott [email protected], Richard Trendall, Thomas Tran
Barndorff-Nielsen, O. and Bl<c3><a6>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<c3><a6>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.
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