# Distribution: Normal Inverse Gaussian 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 | ```
nigtransform(mu = 0, sigma = 1, skew = 0, shape = 3)
``` |

### 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` |
The conditional non-time varying skewness and shape parameters estimated from the GARCH process (zeta-rho). |

### Details

The NIG transformation is taken from Rmetrics internal function and scaled as shown 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 NIG distribution functions.

### Author(s)

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

Alexios Ghalanos for rgarch implementation.

### References

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

Eberlein, E. and Prauss, K., *The Generalized Hyperbolic Model Financial
Derivatives and Risk Measures*, 1998, Mathematical Finance, Bachelier Congress
2000.