Generalized Hyperbolic Student-t Moments

Description

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

Usage

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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)

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.

Value

a numerical value.

Author(s)

Diethelm Wuertz.

References

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

Examples

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## 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)

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