Moments for the Normal Inverse Gaussian

Computes the first four moments for the normal inverse Gaussian distribution.

Usage

nigMean(alpha = 1, beta = 0, delta = 1, mu = 0)
nigVar(alpha = 1, beta = 0, delta = 1, mu = 0)
nigSkew(alpha = 1, beta = 0, delta = 1, mu = 0)
nigKurt(alpha = 1, beta = 0, delta = 1, mu = 0)

Arguments

alpha

shape parameter.

beta

skewness parameter beta, 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 mean, var, skew, or kurt, obtained by dropping the nig prefix from the name of the corresponding function and lowercasing it.

References

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

Author

Diethelm Wuertz.

Examples

## nigMean -
   # Median:
   nigMean(alpha = 1, beta = 0, delta = 1, mu = 0)
#> mean 
#>    0 
 
## nigVar - 
   # Inter-quartile Range:
   nigVar(alpha = 1, beta = 0, delta = 1, mu = 0)
#> var 
#>   1 
 
## nigSKEW -  
   # Robust Skewness:
   nigSkew(alpha = 1, beta = 0, delta = 1, mu = 0)
#> skew 
#>    0 
   
## nigKurt -
   # Robust Kurtosis:
   nigKurt(alpha = 1, beta = 0, delta = 1, mu = 0)
#> kurt 
#>    3