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Most discrete count models (poisson, nbd and the likes) are only defined for non-negative counts.

If I have negative counts — how should these models be used?

  • Would it for instance be OK to just "shift" the distributions with a constant representing the minimum value and then back again for predictions?

  • Are there any count distributions that can be specifically used for modelling negative data?

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    $\begingroup$ Just out of curiousity, what would a negative count be a count of? $\endgroup$ – IWS Aug 30 '17 at 10:52
  • $\begingroup$ @IWS e.g. CrossValidated ratings. $\endgroup$ – salient Aug 30 '17 at 11:29
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    $\begingroup$ When you say "negative counts" do you mean "a difference between two sets of counts" (which result can be negative or positive or 0)? For example, you could consider the overall votes on a question or answer to be the difference between the number of upvotes and number of downvotes. If so, could you not simply model it as the difference of two count distributions (negative binomial perhaps, or even Fisher series distributions), perhaps with zero-inflation? There's the Skellam (difference of two Poissons) but I doubt that would be heavy tailed enough. ... $\endgroup$ – Glen_b Aug 30 '17 at 11:31

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