fBasics (version 4021.93)

ghMoments: Generalized Hyperbolic Distribution Moments

Description

Calculates moments of the generalized hyperbolic distribution function

Usage

ghMean(alpha=1, beta=0, delta=1, mu=0, lambda=-1/2)
ghVar(alpha=1, beta=0, delta=1, mu=0, lambda=-1/2)
ghSkew(alpha=1, beta=0, delta=1, mu=0, lambda=-1/2)
ghKurt(alpha=1, beta=0, delta=1, mu=0, lambda=-1/2)
ghMoments(order, type = c("raw", "central", "mu"),
    alpha = 1, beta=0, delta=1, mu=0, lambda=-1/2)

Value

a numerical value.

Arguments

alpha, beta, delta, mu, lambda

numeric values. alpha is the first shape parameter; beta is the second shape parameter in the range (0, alpha); delta is the scale parameter, must be zero or positive; mu is the location parameter, by default 0; and lambda defines the sublclass, by default -1/2.

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

## ghMean -
   ghMean(alpha=1.1, beta=0.1, delta=0.8, mu=-0.3, lambda=1)
   
## ghKurt -
   ghKurt(alpha=1.1, beta=0.1, delta=0.8, mu=-0.3, lambda=1)
   
## ghMoments -
   ghMoments(4, 
     alpha=1.1, beta=0.1, delta=0.8, mu=-0.3, lambda=1)
   ghMoments(4, "central",
     alpha=1.1, beta=0.1, delta=0.8, mu=-0.3, lambda=1)