ghypChangePars: Change Parameterizations of the Generalized Hyperbolic...

ghypChangeParsR Documentation

Change Parameterizations of the Generalized Hyperbolic Distribution


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)



The set of parameters to change from.


The set of parameters to change to.


"from" parameter vector consisting of 5 numerical elements.


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, Jennifer Tso, Richard Trendall


Barndorff-Nielsen, O. and Bl<e6>sild, 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



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

HyperbolicDist documentation built on March 18, 2022, 6:23 p.m.