# ghypMom: Calculate Moments of the Generalized Hyperbolic Distribution In HyperbolicDist: The Hyperbolic Distribution

 ghypMom R Documentation

## Calculate Moments of the Generalized Hyperbolic Distribution

### Description

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.

### Usage

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

### Arguments

 `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 `c(lambda, alpha, beta, delta, mu)` (see `dghyp`). `momType` Common types of moments to be calculated, default is "raw". See Details. `about` Numeric. The point around which the moment is to be calculated, default is 0. See Details.

### Details

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, W<fc>rtz and Tran (2008).

### Value

The moment specified.

### Author(s)

David Scott d.scott@auckland.ac.nz

### References

Scott, D. J., W<fc>rtz, D. and Tran, T. T. (2008) Moments of the Generalized Hyperbolic Distribution. Preprint.

`ghypChangePars`, `is.wholenumber`, `momChangeAbout`, `momIntegrated`, `ghypMean`, `ghypVar`, `ghypSkew`, `ghypKurt`.

### Examples

```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)

```

HyperbolicDist documentation built on March 18, 2022, 6:23 p.m.