Multivariate Generalized Gaussian Distribution (MGGD)

We present the code for generating realizations from the MGGD [1] as well as estimating its parameters [2]. The MGGD can be characterized using two parameters, the scatter matrix and the shape parameter. If the shape parameter is less than 1 the distribution of the marginals is super-Gaussian (i.e. more peaky, with heavier tails) and if the shape parameter is greater than 1, the distribution of the marginals is sub-Gaussian (i.e., less peaky with lighter tails). If shape parameter is equal to 1, then we generate multivariate Gaussian sources.


[1] E. Gomez, M. Gomez-Viilegas, and J. Marin, "A multivariate generalization of the power exponential family of distributions," Communications in Statistics-Theory and Methods, vol. 27, no. 3, pp. 589-600, 1998.

[2] Z. Boukouvalas, S. Said, L. Bombrun, Y. Berthoumieu, and T. Adali, " A new Riemannian averaged fixed-point algorithm for MGGD parameter estimation," IEEE Signal Proc. Letts., vol. 22, no. 12, pp. 2314-2318, Dec. 2015.