Robust Moments for the GHT

Computes the first four robust moments for the generalized hyperbolic Student-t.

Usage

ghtMED(beta = 0.1, delta = 1, mu = 0, nu = 10)
ghtIQR(beta = 0.1, delta = 1, mu = 0, nu = 10)
ghtSKEW(beta = 0.1, delta = 1, mu = 0, nu = 10)
ghtKURT(beta = 0.1, delta = 1, mu = 0, nu = 10)

Arguments

beta

skewness parameter in the range (0, alpha).

delta

scale parameter, must be zero or positive.

mu

location parameter, by default 0.

nu

a numeric value, the number of degrees of freedom. Note, alpha takes the limit of abs(beta), and lambda=-nu/2.

Details

The parameters are those of the first parameterization.

Value

a named numerical value. The name is one of MED, IQR, SKEW, or KURT, obtained by dropping the ght prefix from the name of the corresponding function.

Author

Diethelm Wuertz.

Examples

## ghtMED -
   # Median:
   ghtMED(beta = 0.1, delta = 1, mu = 0, nu = 10)
#>        MED 
#> 0.01111361 

## ghtIQR -
   # Inter-quartile Range:
   ghtIQR(beta = 0.1, delta = 1, mu = 0, nu = 10)
#>     IQR 
#> 0.44269 

## ghtSKEW -
   # Robust Skewness:
   ghtSKEW(beta = 0.1, delta = 1, mu = 0, nu = 10)
#>        SKEW 
#> 0.002441764 

## ghtKURT -
   # Robust Kurtosis:
   ghtKURT(beta = 0.1, delta = 1, mu = 0, nu = 10)
#>    KURT 
#> 1.27687