fBasics (version 4021.93)

hypMoments: Hyperbolic distribution moments

Description

Calculates moments of the hyperbolic distribution function.

Usage

hypMean(alpha=1, beta=0, delta=1, mu=0)
hypVar(alpha=1, beta=0, delta=1, mu=0)
hypSkew(alpha=1, beta=0, delta=1, mu=0)
hypKurt(alpha=1, beta=0, delta=1, mu=0)
hypMoments(order, type = c("raw", "central", "mu"),
    alpha=1, beta=0, delta=1, mu=0)

Value

a numerical value

Arguments

alpha, beta, delta, mu

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.

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

## hypMean -
   hypMean(alpha=1.1, beta=0.1, delta=0.8, mu=-0.3)
   
## ghKurt -
   hypKurt(alpha=1.1, beta=0.1, delta=0.8, mu=-0.3)
   
## hypMoments -
   hypMoments(4, alpha=1.1, beta=0.1, delta=0.8, mu=-0.3)
   hypMoments(4, "central", alpha=1.1, beta=0.1, delta=0.8, mu=-0.3)