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)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
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 hyperbChangePars to
transfer between parameterizations.
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.
David Scott d.scott@auckland.ac.nz, Richard Trendall, Thomas Tran
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.
dhyperb,
hyperbMean,hyperbChangePars,
besselK