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.
2.
3.
4.
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 |
Details
In the 4 parameterizations, the following must be positive:
1.
2.
3.
4.
Furthermore, note that in the first parameterization
must be greater than the absolute value of
; in the third parameterization,
must be less than one, and the absolute value of
must
be less than
; and in the fourth parameterization,
must be greater than the absolute value of
.
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
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