ghypMom | R Documentation |

This function can be used to calculate raw moments, mu moments, central moments and moments about any other given location for the generalized hyperbolic distribution.

```
ghypMom(order, Theta, momType = "raw", about = 0)
```

`order` |
Numeric. The order of the moment to be calculated. Not permitted to be a vector. Must be a positive whole number except for moments about zero. |

`Theta` |
Numeric. The parameter vector specifying the GIG
distribution. Of the form |

`momType` |
Common types of moments to be calculated, default is "raw".
See |

`about` |
Numeric. The point around which the moment is to be
calculated, default is 0. See |

Checking whether `order`

is a whole number is carried out using
the function `is.wholenumber`

.

`momType`

can be either "raw" (moments about zero), "mu" (moments
about mu), or "central" (moments about mean). If one of these moment
types is specified, then there is no need to specify the `about`

value. For moments about any other location, the `about`

value
must be specified. In the case that both `momType`

and
`about`

are specified and contradicting, the function will always
calculate the moments based on `about`

rather than
`momType`

.

To calculate moments of the generalized hyperbolic distribution, the
function first calculates mu moments by the formula defined below and
then transforms mu moments to central moments or raw moments or
moments about any other location as required by calling
`momChangeAbout`

.

The mu moments are obtained from the recursion formula given in Scott, Würtz and Tran (2008).

The moment specified.

David Scott d.scott@auckland.ac.nz

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

`ghypChangePars`

, `is.wholenumber`

,
`momChangeAbout`

, `momIntegrated`

,
`ghypMean`

, `ghypVar`

, `ghypSkew`

,
`ghypKurt`

.

```
Theta <- c(2,2,1,2,1)
mu <- Theta[5]
### mu moments
(m1 <- ghypMean(Theta))
m1 - mu
ghypMom(1, Theta, momType = "mu")
momIntegrated("ghyp", order = 1, param = Theta, about = mu)
ghypMom(2, Theta, momType = "mu")
momIntegrated("ghyp", order = 2, param = Theta, about = mu)
ghypMom(10, Theta, momType = "mu")
momIntegrated("ghyp", order = 10, param = Theta, about = mu)
### raw moments
ghypMean(Theta)
ghypMom(1, Theta, momType = "raw")
momIntegrated("ghyp", order = 1, param = Theta, about = 0)
ghypMom(2, Theta, momType = "raw")
momIntegrated("ghyp", order = 2, param = Theta, about = 0)
ghypMom(10, Theta, momType = "raw")
momIntegrated("ghyp", order = 10, param = Theta, about = 0)
### central moments
ghypMom(1, Theta, momType = "central")
momIntegrated("ghyp", order = 1, param = Theta, about = m1)
ghypVar(Theta)
ghypMom(2, Theta, momType = "central")
momIntegrated("ghyp", order = 2, param = Theta, about = m1)
ghypMom(10, Theta, momType = "central")
momIntegrated("ghyp", order = 10, param = Theta, about = m1)
```

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