fBasics (version 4021.93)

ghRobMoments: Robust Moments for the GH

Description

Computes the first four robust moments for the generalized hyperbolic distribution..

Usage

ghMED(alpha = 1, beta = 0, delta = 1, mu = 0, lambda = -1/2)
ghIQR(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)

Value

All values for the *gh functions are numeric vectors:

d* returns the density,

p* returns the distribution function,

q* returns the quantile function, and

r* generates random deviates.

All values have attributes named "param" listing the values of the distributional parameters.

Arguments

alpha, beta, delta, mu, lambda

numeric values. alpha is the first shape parameter; beta is the second shape parameter in the range (0, alpha); delta is the scale parameter, must be zero or positive; mu is the location parameter, by default 0; and lambda defines the sublclass, by default -1/2. These are the meanings of the parameters in the first parameterization pm=1 which is the default parameterization. In the second parameterization, pm=2 alpha and beta take the meaning of the shape parameters (usually named) zeta and rho. In the third parameterization, pm=3 alpha and beta take the meaning of the shape parameters (usually named) xi and chi. In the fourth parameterization, pm=4 alpha and beta take the meaning of the shape parameters (usually named) a.bar and b.bar.

Author

Diethelm Wuertz.

Examples

## ghMED -
   # Median:
   ghMED(alpha = 1, beta = 0, delta = 1, mu = 0, lambda = -1/2)

## ghIQR -
   # Inter-quartile Range:
   ghIQR(alpha = 1, beta = 0, delta = 1, mu = 0, lambda = -1/2)

## ghSKEW -
   # Robust Skewness:
   ghSKEW(alpha = 1, beta = 0, delta = 1, mu = 0, lambda = -1/2)

## ghKURT -
   # Robust Kurtosis:
   ghKURT(alpha = 1, beta = 0, delta = 1, mu = 0, lambda = -1/2)