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 Bl<c3><a6>sild (1983), and the fourth in Prause (1999)
The set of parameters to change from.
The set of parameters to change to.
"from" parameter vector consisting of 4 numerical elements.
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
David Scott [email protected], Jennifer Tso, Richard Trendall
Barndorff-Nielsen, O. and Bl<c3><a6>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.
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