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Is the multinomial distribution an example of a multimodal distribution? I was just curious about this. I know of continuous distributions that are multimodal, but didn't know if you could talk about PMFs in the same way.

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Note that the multinomial distribution is a distribution of a random vector, with as many components as the length of the probability vector $p=(p_1, \dotsc,p_k)$. So you need a definition of unimodal/multimodal adapted to the multivariate case. Then it turns out that there is no unique definition of what unimodality (and hence multimodality) means in the multivariate case, see https://projecteuclid.org/euclid.aos/1176343466, so to answer your question you would have to choose definition ...

Still, all the marginals (which are binomial) are unimodal, and I would be surprised if the answer for the multinomial is different. But for an answer, I will have to read that complete paper, and now it is to late night! Coming back ...

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