hyperbChangePars: Change Parameterizations of the Hyperbolic Distribution

Description Usage Arguments Details Value Author(s) References See Also Examples

View source: R/hyperbChangePars.R

Description

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)

Usage

1
hyperbChangePars(from, to, param, noNames = FALSE)

Arguments

from

The set of parameters to change from.

to

The set of parameters to change to.

param

"from" parameter vector consisting of 4 numerical elements.

noNames

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

Details

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.

Value

A numerical vector of length 4 representing param in the to parameterization.

Author(s)

David Scott [email protected], Jennifer Tso, Richard Trendall

References

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.

See Also

dhyperb

Examples

1
2
3
4
param1 <- c(2, 1, 3, 1)                   # Parameterization 1
param2 <- hyperbChangePars(1, 2, param1)   # Convert to parameterization 2
param2                                     # Parameterization 2
hyperbChangePars(2, 1, as.numeric(param2)) # Convert back to parameterization 1

sjp/GeneralizedHyperbolic documentation built on May 26, 2017, 10:13 a.m.