Generalized Hyperbolic Moments and Mode {HyperbolicDist}R Documentation

Moments and Mode of the Generalized Hyperbolic Distribution

Description

Functions to calculate the mean, variance, and mode of a specific generalized hyperbolic distribution.

Usage

ghypMean(Theta)
ghypVar(Theta)
ghypMode(Theta)

Arguments

Theta Parameter vector of the generalized hyperbolic distribution.

Value

ghypMean gives the mean of the generalized hyperbolic distribution, ghypVar the variance, and ghypMode the mode. The formulae used for the mean and variance are as given in Prause (1999). The mode is found by a numerical optimisation using optim.
The parameterisation of the generalized hyperbolic distribution used for these functions is the (alpha,beta) one. See ghypChangePars to transfer between parameterisations.

Author(s)

David Scott d.scott@auckland.ac.nz, Thomas Tran

References

Prause, K. (1999) The generalized hyperbolic models: Estimation, financial derivatives and risk measurement. PhD Thesis, Mathematics Faculty, University of Freiburg.

See Also

dghyp, ghypChangePars, besselK, RLambda.

Examples

Theta <- c(2,2,1,2,2)
ghypMean(Theta)
ghypVar(Theta)
ghypMode(Theta)
maxDens <- dghyp(ghypMode(Theta), Theta)
ghypRange <- ghypCalcRange(Theta, tol = 10^(-3)*maxDens)
curve(dghyp(x, Theta), ghypRange[1], ghypRange[2])
abline(v = ghypMode(Theta), col = "blue")
abline(v = ghypMean(Theta), col = "red")

[Package HyperbolicDist version 0.5-3 Index]