| Specific Generalized Hyperbolic Moments and Mode {HyperbolicDist} | R Documentation |
Moments and Mode of the Generalized Hyperbolic Distribution
Description
Functions to calculate the mean, variance, skewness, kurtosis and mode of a specific generalized hyperbolic distribution.
Usage
ghypMean(Theta)
ghypVar(Theta)
ghypSkew(Theta)
ghypKurt(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, ghypSkew the skewness,
ghypKurt the kurtosis, and ghypMode the mode. The
formulae used for the mean is given in Prause (1999). The variance,
skewness and kurtosis are obtained using the recursive formula
implemented in ghypMom which can calculate moments of
all orders about any point.
The mode is found by a numerical optimisation using
optim. For the special case of the hyperbolic
distribution a formula for the mode is available, see
hyperbMode.
The parameterization of the generalized hyperbolic distribution used
for these functions is the (\alpha,\beta) one. See
ghypChangePars to transfer between parameterizations.
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)
ghypSkew(Theta)
ghypKurt(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")