# dist-ghtMoments: Generalized Hyperbolic Student-t Moments In fBasics: Rmetrics - Markets and Basic Statistics

## Description

Calculates moments of the generalized hyperbbolic Student-t distribution function.

## Usage

 ```1 2 3 4 5 6 7``` ```ghtMean(beta=0.1, delta=1, mu=0, nu=10) ghtVar(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) ghtMoments(order, type = c("raw", "central", "mu"), beta=0.1, delta=1, mu=0, nu=10) ```

## Arguments

 `beta, delta, mu` numeric values. `beta` is the skewness parameter in the range `(0, alpha)`; `delta` is the scale parameter, must be zero or positive; `mu` is the location parameter, by default 0. These are the parameters in the first parameterization. `nu` a numeric value, the number of degrees of freedom. Note, `alpha` takes the limit of `abs(beta)`, and `lambda=-nu/2`. `order` an integer value, the order of the moment. `type` a character value, `"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 numerical value.

Diethelm Wuertz.

## References

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

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12``` ``` ## ghtMean - ghtMean(beta=0.2, delta=1.2, mu=-0.5, nu=4) ## ghtKurt - ghtKurt(beta=0.2, delta=1.2, mu=-0.5, nu=4) ## ghtMoments - ghtMoments(4, beta=0.2, delta=1.2, mu=-0.5, nu=4) ghtMoments(4, "central", beta=0.2, delta=1.2, mu=-0.5, nu=4) ```

fBasics documentation built on Nov. 17, 2017, 2:14 p.m.