# Distribution: Generalized Hyperbolic Transformation and Scaling

### Description

The function scales the distributions from the (0, 1) zeta-rho GARCH parametrization to the alpha-beta parametrization and performs the appropriate scaling to the parameters given the estimated sigma and mu.

### Usage

1 | ```
ghyptransform(mu = 0, sigma = 1, skew = 0, shape = 3, lambda = -0.5)
``` |

### Arguments

`mu` |
Either the conditional time-varying (vector) or unconditional mean estimated from the GARCH process. |

`sigma` |
The conditional time-varying (vector) sigma estimated from the GARCH process. |

`skew, shape, lambda` |
The conditional non-time varying skewness (rho) and shape (zeta) parameters estimated from the GARCH process (zeta-rho), and the GHYP lambda parameter (‘dlambda’ in the estimation). |

### Details

The GHYP transformation is taken from Rmetrics internal function and scaled as in Blaesild (see references).

### Value

A matrix of size nrows(sigma) x 4 of the scaled and transformed parameters to be used in the alpha-beta parametrized GHYP distribution functions.

### Author(s)

Diethelm Wuertz for the Rmetrics **R**-port of the nig transformation function.

Alexios Ghalanos for rugarch implementation.

### References

Blaesild, P. 1981, The two-dimensional hyperbolic distribution and related
distributions, with an application to Johannsen's bean data, *Biometrika*,
**68**, 251–263.

Eberlein, E. and Prauss, K. 2000, The Generalized Hyperbolic Model Financial
Derivatives and Risk Measures, *Mathematical Finance Bachelier Congress*,
245–267.