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I'm doing a lot of work on the Wikipedia page for this distribution:

http://en.wikipedia.org/wiki/Dirichlet_compound_multinomial_distribution

The actual name of the page is "Multivariate Pólya distribution". However, in the text I've been writing, I actually use "Dirichlet compound multinomial distribution", abbreviated to DCM. I've also seen just "Dirichlet-multinomial distribution".

Which one is the most used?

The Google search test reveals:

  • 20,000+ for "multivariate polya"
  • 46,000+ for "dirichlet compound multinomial"
  • 24,000+ for "dirichlet multinomial"
  • 30,000+ for "dirichlet multinomial distribution"

But this doesn't really tell us anything, esp. given the non-intuitive values of the last two searches.

My sense is that "Multivariate Polya" (with or without the accent) is the least used, but this is just an intuition.

Also, if we call it "Dirichlet-multinomial distribution", how do we abbreviate it, e.g. in a mathematical description? DM(), DirMult()? Or is it just left as-is?

Note also that the article "Estimating a Dirichlet distribution" by Thomas P. Minka calls it simply the "Polya distribution". (Or rather, he introduces it as the "Dirichlet-multinomial distribution", with "Polya distribution" as a synonym, but then uses the latter term in the rest of the discussion.) However, the term "Polya distribution" seems to have lots of other possible definitions referring to various quite distinct distributions, so this name is not good as the canonical name.

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Given google's nature of eliminating uncommon words from search strings, if you want to get search counts for specific strings, you need to enclose them in quotes.

doing that, i get around 3k for multivariate polya, 3.9k for dirichlet compound multinomial, 20k for dirichlet multinomial, and ~8k for dirichlet multinomial distribution.

Thus, I say Dirichlet Multinomial...adding "distribution" is optional.

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