fBasics (version 2110.79)

ghMoments: Generalized Hyperbolic Distribution Moments

Description

Calculates moments of the generalized hyperbbolic 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)

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;

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.

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)