hypMoments {fBasics}R Documentation

Hyperbolic Distribution Moments

Description

Calculates moments of the hyperbbolic 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)

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.

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

   
## 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)
[Package fBasics version 2160.81 Index]