Functions used to calculate the mean, variance, skewness and kurtosis of a hyperbolic distribution. Not expected to be called directly by users.
RLambda(zeta, lambda = 1)
SLambda(zeta, lambda = 1)
MLambda(zeta, lambda = 1)
WLambda1(zeta, lambda = 1)
WLambda2(zeta, lambda = 1)
WLambda3(zeta, lambda = 1)
WLambda4(zeta, lambda = 1)
gammaLambda1(hyperbPi, zeta, lambda = 1)
gammaLambda1(hyperbPi, zeta, lambda = 1)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.
The functions RLambda and SLambda 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 Bl<e6>sild,
P. (1981) for details of the calculations.
The parameterization of the hyperbolic distribution used for this
and other components of the HyperbolicDist package is the
\((\pi,\zeta)\) one. See hyperbChangePars to
transfer between parameterizations.
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.