I need to fit a generalized Gaussian distribution to a 7-dim cloud of points containing quite a significant number of outliers with high leverage. Do you know any good R package for this job?
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One caution, though: mixture modelling in high dimensional space can get pretty CPU and memory intensive if your cloud of points is large. About four years ago I was doing a batch of 11-dimensional, 50-200K point data, and it was tending to run into 4-11GB of RAM and take up to a week to compute for each case (and I had 400). This is certainly possible, but can be a headache if you're using a shared compute cluster or have limited resources available.
This sounds like a classic multivariate Gaussian Mixture Model. I think that the BayesM package might work.
Here are some multivariate Gaussian Mixture packages