hyperbChangePars function

Change Parameterizations of the Hyperbolic Distribution

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

1. $pi, zeta, delta, mu$

2. $alpha, beta, delta, mu$

3. $phi, gamma, delta, mu$

4. $xi, chi, delta, mu$

The first three are given in Barndorff-Nielsen and (1983), and the fourth in Prause (1999)

hyperbChangePars(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 4 numerical elements.
• noNames: Logical. When TRUE, suppresses the parameter names in the output.

Details

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 $xi$.

Returns

A numerical vector of length 4 representing Theta 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

dhyperb

Examples

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