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I learned from this answer that:

A mixture distribution combines different component distributions with weights that typically sum to one (or can be renormalized). A gaussian-mixture is the special case where the components are Gaussians.

And I learned from this tutorial that:

A Gaussian mixture model (GMM) is useful for modeling data that comes from one of several groups: the groups might be different from each other, but data points within the same group can be well-modeled by a Gaussian distribution.

So far as I know, we combine several Gaussina models with some weights for each to fit the true distribution in the data where there are some variables, like the mean of each Gaussian, being unknown.

My question is that given that GMM is a only special case where the components are Gaussians could anyone please show that in which scenarios GMM is not appropriate? And when we prefer Gaussian distributions over any other distributions?

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