# ghypChangePars: Change Parameterizations of the Generalized Hyperbolic... In HyperbolicDist: The Hyperbolic Distribution

 ghypChangePars R Documentation

## Change Parameterizations of the Generalized Hyperbolic Distribution

### Description

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, \bar\alpha, \bar\beta, \delta, \mu

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 TRUE, suppresses the parameter names in the output.

### Details

In the 4 parameterizations, the following must be positive:

1. \alpha, \delta

2. \zeta, \delta

3. \xi, \delta

4. \bar\alpha, \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, \bar\alpha must be greater than the absolute value of \bar\beta.

### 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.

dghyp

### 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


HyperbolicDist documentation built on Nov. 26, 2023, 9:07 a.m.