hyperbChangePars: Change Parameterizations of the Hyperbolic Distribution

hyperbChangeParsR Documentation

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 Bl<e6>sild (1983), and the fourth in Prause (1999)


hyperbChangePars(from, to, Theta, noNames = FALSE)



The set of parameters to change from.


The set of parameters to change to.


"from" parameter vector consisting of 4 numerical elements.


Logical. When TRUE, suppresses the parameter names in the output.


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 Theta in the to parameterization.


David Scott d.scott@auckland.ac.nz, 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(-2,1,3,0)                      # 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

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