GED (Multivariate)

This is a multivariate generalization of the Generalized Error Distribution. As with the multivariate Normal and multivariate t, this has a constant density on ellipses, where the density declines as the distance from zero increases.

Parameters	2. \(c \) (shape) and covariance matrix \(\Sigma\).
Kernel	\(\exp \left( { - \frac{1}{2}{{\left( {\frac{{{\bf{x'}}{\Sigma ^{ - 1}}{\bf{x}}}}{{{b^2}}}} \right)}^{1/c}}} \right)\) \(b\) is a function of the shape \(c\) which standardizes the distribution to make \(\Sigma\) the covariance matrix.
Support	\(\mathbb{R}^{n}\)
Mean	0 (a mean shift is simple, but rarely needed)
Covariance	\(\Sigma\)
Main Uses	In financial econometrics, as an alternative to the multivariate t as the distribution of errors to provide different tail behavior from the Normal. It's fatter-tailed than the Normal if \(c > 1\) and thinner-tailed if \(c < 1\).
Density Function	%LOGGEDDENSITY(x,c,covariance)