ghypChangePars {HyperbolicDist} | R Documentation |
This function interchanges between the following 4 parameterizations of the generalized hyperbolic distribution:
1. lambda, alpha, beta, delta, mu
2. lambda, zeta, rho, delta, mu
3. lambda, xi, chi, delta, mu
4. lambda, alpha bar, beta bar, delta, mu
These are the parameterizations given in Prause (1999)
ghypChangePars(from, to, Theta, noNames = FALSE)
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. |
In the 4 parameterizations, the following must be positive:
1. alpha, delta
2. zeta, delta
3. xi, delta
4. alpha bar, 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.
A numerical vector of length 5 representing Theta
in the
to
parameterization.
David Scott d.scott@auckland.ac.nz, Jennifer Tso, Richard Trendall
Barndorff-Nielsen, O. and Blęsild, 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.
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