Robust moments for the HYP

Computes the first four robust moments for the hyperbolic distribution.

Usage

hypMED(alpha = 1, beta = 0, delta = 1, mu = 0)
hypIQR(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)

Arguments

alpha

shape parameter, a positive number. alpha can also be a vector of length four, containing alpha, beta, delta and mu (in that order).

beta

skewness parameter, abs(beta) is in the range (0, alpha).

delta

scale parameter, must be zero or positive.

mu

location parameter, by default 0.

Value

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

Author

Diethelm Wuertz

Examples

## hypMED -
   # Median:
   hypMED(alpha = 1, beta = 0, delta = 1, mu = 0)
#>          MED 
#> 1.830888e-10 

## hypIQR -
   # Inter-quartile Range:
   hypIQR(alpha = 1, beta = 0, delta = 1, mu = 0)
#>      IQR 
#> 1.848932 

## hypSKEW -
   # Robust Skewness:
   hypSKEW(alpha = 1, beta = 0, delta = 1, mu = 0)
#>         SKEW 
#> 6.827298e-11 

## hypKURT -
   # Robust Kurtosis:
   hypKURT(alpha = 1, beta = 0, delta = 1, mu = 0)
#>     KURT 
#> 1.383927