# hyperbChangePars: Change Parameterizations of the Hyperbolic Distribution In HyperbolicDist: The Hyperbolic Distribution

 hyperbChangePars R Documentation

## Change Parameterizations of the Hyperbolic Distribution

### Description

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)

### Usage

```hyperbChangePars(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 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 `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.

`dhyperb`

### Examples

```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.