Generalized Hyperbolic Distribution Moments

Calculates moments of the generalized hyperbolic distribution.

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: 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.
lambda: numeric value, defines the sublclass, by default \(-1/2\).
order: an integer value, the order of the moment.
type: a character value, "raw" gives the moments about zero, "central" gives the central moments about the mean, and "mu" gives 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 nig prefix from the name of the corresponding function and lowercasing it.

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

References

Scott, D. J., Wuertz, D. and Tran, T. T. (2008) Moments of the Generalized Hyperbolic Distribution. Preprint.

Author

Diethelm Wuertz

Examples

## ghMean -
   ghMean(alpha=1.1, beta=0.1, delta=0.8, mu=-0.3, lambda=1)
#>        mean 
#> -0.08410502 
   
## ghKurt -
   ghKurt(alpha=1.1, beta=0.1, delta=0.8, mu=-0.3, lambda=1)
#>     kurt 
#> 2.044599 
   
## ghMoments -
   ghMoments(4, 
     alpha=1.1, beta=0.1, delta=0.8, mu=-0.3, lambda=1)
#>    m4raw 
#> 23.96634 
   ghMoments(4, "central",
     alpha=1.1, beta=0.1, delta=0.8, mu=-0.3, lambda=1)
#> m4central 
#>  24.18639