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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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You will find links to at least four R packages for identifying multivariate outliers in the replies to a similar question at stats.stackexchange.com/questions/213/…. That might be a good start. – whuber Jul 7 '11 at 13:51

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This sounds like a classic multivariate Gaussian Mixture Model. I think that the BayesM package might work.

Here are some multivariate Gaussian Mixture packages - bayesm: cran.r-project.org/web/packages/bayesm/index.html - mixtools: www.jstatsoft.org/v32/i06/paper

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