hyperb.mean {HyperbolicDist}R Documentation

Mean, Variance and Mode of the Hyperbolic Distribution

Description

Functions to calculate the mean, variance, and mode of a specific hyperbolic distribution. R.lambda and S.lambda are functions derived from Bessel functions which are used in the calculation of the mean and variance.

Usage

hyperb.mean(theta)
hyperb.var(theta)
hyperb.mode(theta)
R.lambda(zeta, lambda = 1)
S.lambda(zeta, lambda = 1)

Arguments

theta Parameter vector of the hyperbolic distribution
zeta Value of the parameter zeta of the hyperbolic distribution
lambda Parameter related to order of Bessel functions

Value

hyperb.mean gives the mean of the hyperbolic distribution, hyperb.var the variance, and hyperb.mode the mode. The formulae used are as given in Barndorff-Nielsen and Blaesild (1983), p. 702. The functions R.lambda and S.lambda 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 parameterisation of the hyperbolic distribution used for this and other components of the hyperbolic package is the pi/zeta one. See hyperb.change.pars to transfer between parameterisations.

Author(s)

David Scott d.scott@auckland.ac.nz, Richard Trendall

References

Barndorff-Nielsen, O. and Blaesild, 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, hyperb.change.pars, besselK

Examples

theta <- c(2,2,2,2)
hyperb.mean(theta)
hyperb.var(theta)
hyperb.mode(theta)

[Package HyperbolicDist version 0.0-1 Index]