fBasics (version 4021.93)

ghtMoments: Generalized Hyperbolic Student-t Moments

Description

Calculates moments of the generalized hyperbolic Student-t distribution function.

Usage

ghtMean(beta=0.1, delta=1, mu=0, nu=10)
ghtVar(beta=0.1, delta=1, mu=0, nu=10)
ghtSkew(beta=0.1, delta=1, mu=0, nu=10)
ghtKurt(beta=0.1, delta=1, mu=0, nu=10)
ghtMoments(order, type = c("raw", "central", "mu"),
    beta=0.1, delta=1, mu=0, nu=10)

Value

a numerical value.

Arguments

beta, delta, mu

numeric values. beta is the skewness parameter in the range (0, alpha); delta is the scale parameter, must be zero or positive; mu is the location parameter, by default 0. These are the parameters in the first parameterization.

nu

a numeric value, the number of degrees of freedom. Note, alpha takes the limit of abs(beta), and lambda=-nu/2.

order

an integer value, the order of the moment.

type

a character value, "raw" returns the moments about zero, "central" returns the central moments about the mean, and "mu" returns the moments about the location parameter mu.

Author

Diethelm Wuertz.

References

Scott, D.J., Wuertz, D. and Tran, T.T. (2008) Moments of the Generalized Hyperbolic Distribution. Preprint.

Examples

## ghtMean -
   ghtMean(beta=0.2, delta=1.2, mu=-0.5, nu=4)
   
## ghtKurt -
   ghtKurt(beta=0.2, delta=1.2, mu=-0.5, nu=4)
   
## ghtMoments -
   ghtMoments(4, 
     beta=0.2, delta=1.2, mu=-0.5, nu=4)
   ghtMoments(4, "central",
     beta=0.2, delta=1.2, mu=-0.5, nu=4)