ghypChangePars function

Change Parameterizations of the Generalized Hyperbolic Distribution

This function interchanges between the following 5 parameterizations of the generalized hyperbolic distribution:

1. $mu, delta, alpha, beta, lambda$

2. $mu, delta, rho, zeta, lambda$

3. $mu, delta, xi, chi, lambda$

4. c("$$", "$\n$", "$mu, delta, alpha bar, beta bar, lambda$")

5. $mu, delta, pi, zeta, lambda$

The first four are the parameterizations given in Prause (1999). The final parameterization has proven useful in fitting.

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

Arguments

• from: The set of parameters to change from.
• to: The set of parameters to change to.
• param: "from" parameter vector consisting of 5 numerical elements.
• noNames: Logical. When TRUE, suppresses the parameter names in the output.

Details

In the 5 parameterizations, the following must be positive:

1. $alpha, delta$

2. $zeta, delta$

3. $xi, delta$

4. $alpha bar, delta$

5. $zeta, delta$

Furthermore, note that in the first parameterization $alpha$ must be greater than the absolute value of $beta$; in the third parameterization, $xi$

must be less than one, and the absolute value of $chi$ must be less than $xi$; and in the fourth parameterization, $alpha bar$ must be greater than the absolute value of $beta bar$.

Returns

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

References

Barndorff-Nielsen, O. and , 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.

Author(s)

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

See Also

dghyp

Examples

param1 <- c(0, 3, 2, 1, 2)               # Parameterization 1
param2 <- ghypChangePars(1, 2, param1)   # Convert to parameterization 2
param2                                   # Parameterization 2
ghypChangePars(2, 1, param2)             # Back to parameterization 1