dist-hypMoments: Hyperbolic distribution moments

In fBasics: Rmetrics - Markets and Basic Statistics

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)

Arguments

alpha	numeric value, the first shape parameter.
beta	numeric value, the second shape parameter in the range (0, alpha).
delta	numeric value, the scale parameter, must be zero or positive.
mu	numeric value, the location parameter, by default 0.
order	an integer value, the order of the moment.
type	a character string, "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 named numerical value. The name is one of mean, var, skew, or kurt, obtained by dropping the hyp prefix from the name of the corresponding function and lowercasing it.

for hypMoments, the name is obtained by paste0("m", order, type).

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)

fBasics documentation built on Sept. 11, 2024, 6:34 p.m.