| ghypMom {HyperbolicDist} | 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 |
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, Würtz and Tran (2008).
Value
The moment specified.
Author(s)
David Scott d.scott@auckland.ac.nz
References
Scott, D. J., Würtz, D. and Tran, T. T. (2008) Moments of the Generalized Hyperbolic Distribution. Preprint.
See Also
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)