hyperbChangePars: Change Parameterizations of the Hyperbolic Distribution
In sjp/GeneralizedHyperbolic: The generalized hyperbolic distribution

Description Usage Arguments Details Value Author(s) References See Also Examples

This function interchanges between the following 4 parameterizations of the hyperbolic distribution:

1. mu, delta, pi, zeta

2. mu, delta, alpha, beta

3. mu, delta, phi, gamma

4. mu, delta, xi, chi

The first three are given in Barndorff-Nielsen and Bl<c3><a6>sild (1983), and the fourth in Prause (1999)

1	hyperbChangePars(from, to, param, noNames = FALSE)

`from`	The set of parameters to change from.
`to`	The set of parameters to change to.
`param`	"from" parameter vector consisting of 4 numerical elements.
`noNames`	Logical. When `TRUE`, suppresses the parameter `names` in the output.

In the 4 parameterizations, the following must be positive:

1. zeta, delta

2. alpha, delta

3. phi, gamma, delta

4. xi, delta

Furthermore, note that in the second parameterization alpha must be greater than the absolute value of beta, while in the fourth parameterization, xi must be less than one, and the absolute value of chi must be less than xi.

A numerical vector of length 4 representing param in the to parameterization.

David Scott d.scott@auckland.ac.nz, Jennifer Tso, Richard Trendall

Barndorff-Nielsen, O. and Bl<c3><a6>sild, P. (1983). Hyperbolic distributions. In Encyclopedia of Statistical Sciences, eds., Johnson, N. L., Kotz, S. and Read, C. B., Vol. 3, pp. 700–707. New York: Wiley.

Prause, K. (1999) The generalized hyperbolic models: Estimation, financial derivatives and risk measurement. PhD Thesis, Mathematics Faculty, University of Freiburg.

dhyperb

param1 <- c(2, 1, 3, 1)                   # Parameterization 1
param2 <- hyperbChangePars(1, 2, param1)   # Convert to parameterization 2
param2                                     # Parameterization 2
hyperbChangePars(2, 1, as.numeric(param2)) # Convert back to parameterization 1