Generalized Hyperbolic Moments and Mode {HyperbolicDist} | R Documentation |
Functions to calculate the mean, variance, and mode of a specific generalized hyperbolic distribution.
ghypMean(Theta) ghypVar(Theta) ghypMode(Theta)
Theta |
Parameter vector of the generalized hyperbolic distribution. |
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.
David Scott d.scott@auckland.ac.nz, Thomas Tran
Prause, K. (1999) The generalized hyperbolic models: Estimation, financial derivatives and risk measurement. PhD Thesis, Mathematics Faculty, University of Freiburg.
dghyp
, ghypChangePars
,
besselK
, RLambda
.
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")