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.

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