ghypChangePars {HyperbolicDist}R Documentation

Change Parameterizations of the Generalized Hyperbolic Distribution

Description

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

1. λ,α,β,δ,μ\lambda, \alpha, \beta, \delta, \mu

2. λ,ζ,ρ,δ,μ\lambda, \zeta, \rho, \delta, \mu

3. λ,ξ,χ,δ,μ\lambda, \xi, \chi, \delta, \mu

4. λ,αˉ,βˉ,δ,μ\lambda, \bar\alpha, \bar\beta, \delta, \mu

These are the parameterizations given in Prause (1999)

Usage

ghypChangePars(from, to, Theta, noNames = FALSE)

Arguments

from

The set of parameters to change from.

to

The set of parameters to change to.

Theta

"from" parameter vector consisting of 5 numerical elements.

noNames

Logical. When TRUE, suppresses the parameter names in the output.

Details

In the 4 parameterizations, the following must be positive:

1. α,δ\alpha, \delta

2. ζ,δ\zeta, \delta

3. ξ,δ\xi, \delta

4. αˉ,δ\bar\alpha, \delta

Furthermore, note that in the first parameterization α\alpha must be greater than the absolute value of β\beta; in the third parameterization, ξ\xi must be less than one, and the absolute value of χ\chi must be less than ξ\xi; and in the fourth parameterization, αˉ\bar\alpha must be greater than the absolute value of βˉ\bar\beta.

Value

A numerical vector of length 5 representing Theta in the to parameterization.

Author(s)

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

References

Barndorff-Nielsen, O. and Blæsild, 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.

See Also

dghyp

Examples

Theta1 <- c(2,2,1,3,0)                   # Parameterization 1
Theta2 <- ghypChangePars(1, 2, Theta1)   # Convert to parameterization 2
Theta2                                   # Parameterization 2
ghypChangePars(2, 1, as.numeric(Theta2)) # Convert back to parameterization 1

[Package HyperbolicDist version 0.6-5 Index]