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I have data set X = {x_1, x_2, \ldots, x_N}, each x_i is a d-dimensional vector, where scalars are from some finite field (In practice they are categories, represented by integers from 1...C).

If my data would be 1-d, then multinomial density would be ok to model it. How do I extend it to multidimensional case? If scalars in vector are iid, then I guess, I could just model it by d-product of multinomial densities? Did I miss something?

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closed as off-topic by Ricardo Andrade, j.c., Andrey Rekalo, Stefan Kohl, Chris Godsil Nov 28 '13 at 14:55

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "This question does not appear to be about research level mathematics within the scope defined in the help center." – Ricardo Andrade, j.c., Andrey Rekalo, Stefan Kohl, Chris Godsil
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up vote 1 down vote accepted

Yes, in the case that they're independent (they need not be identically distributed), simply multiply the mass densities together to get the mass density of the d-dimensional vector.

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