# 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, alpha bar, beta bar, 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. 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.

### 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 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.

`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 March 18, 2022, 6:23 p.m.