Hyperbolic distribution moments

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).

References

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

Author

Diethelm Wuertz

Examples

## hypMean -
   hypMean(alpha=1.1, beta=0.1, delta=0.8, mu=-0.3)
#>        mean 
#> -0.08410502 
   
## ghKurt -
   hypKurt(alpha=1.1, beta=0.1, delta=0.8, mu=-0.3)
#>     kurt 
#> 2.044599 
   
## hypMoments -
   hypMoments(4, alpha=1.1, beta=0.1, delta=0.8, mu=-0.3)
#>    m4raw 
#> 23.96634 
   hypMoments(4, "central", alpha=1.1, beta=0.1, delta=0.8, mu=-0.3)
#> m4central 
#>  24.18639