RLambda: Functions for Calculating Moments

In GeneralizedHyperbolic: The Generalized Hyperbolic Distribution

Functions for Calculating Moments

Description

Functions used to calculate the mean, variance, skewness and kurtosis of a hyperbolic distribution. Not expected to be called directly by users.

Usage

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)

Arguments

hyperbPi	Value of the parameter \pi of the hyperbolic distribution.
zeta	Value of the parameter \zeta of the hyperbolic distribution.
lambda	Parameter related to order of Bessel functions.

Value

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 Blæsild, 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.

Author(s)

David Scott [e-mail], Richard Trendall, Thomas Tran

References

Barndorff-Nielsen, O. and Blæsild, 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 Blæsild, 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.

See Also

dhyperb, hyperbMean,hyperbChangePars, besselK

GeneralizedHyperbolic documentation built on Nov. 26, 2023, 5:07 p.m.