Change Parameterizations of the Hyperbolic Distribution
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 Blæsild (1983), and the fourth in Prause (1999)
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 |
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 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.
param1 <- c(2, 1, 3, 1) # Parameterization 1 param2 <- hyperbChangePars(1, 2, param1) # Convert to parameterization 2 param2 # Parameterization 2 hyperbChangePars(2, 1, param2) # Back to parameterization 1
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