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I have several set of probability distributions. I want to reliably estimate consistency across distributions inside each set.

Literature contains methods to compare two distributions: Kullback-Leibler divergence, earth mover's distance, ... But I couldn't find anything for more than two distributions.

I can imagine an indice built on top of one of these methods. For example, I could first merge all probability distributions into a single one. And then use the mean (or median) of the symmetric KL (or any other distance/divergence/...) between the merged distribution and all others distributions in the considered set. But before starting something out of the blue, I would rather be sure that nothing already exists.

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