You ignored my point that each independent coin toss trial outcome is
uniformly distributed whereas the Poisson distribution is
exponentially distributed.
That is why I asserted that your and xulescu's analogies are inapplicable. Rare trial outcomes in a Poisson distribution occur less often then less rare ones (look at the area under the distribution curve at the tails). Whereas all trial outcomes in a coin toss occur at the same probability.
Ah *snooze*.
Do you really think we're idiots? The analogy was for an error in your modelling that you yourself accepted as valid, not for the numbers. To my models it makes no difference whatsoever if they're coin tosses, loaded D20's or, indeed, exponentials or Poisson.
To address your point directly, a uniform distribution CANNOT have a tail by definition. You must be meaning the distribution of complex events, AKA counts. You continue to ignore permutations and epsilon-variants even if they show up in your model as well. In terms of counts, both Poisson and binary distributions have normal tails.
Both also completely fail because they assume complete independence between the samples.
In the meanwhile you keep wasting your time on this triviality. THIS IS NOT THE MOST PRODUCTIVE USE OF YOUR TIME. Please let this one thing go and focus. We appreciate your help, but all this energy expended on a model, we all agree is not predictive, only accelerates the heat death of this thread. Your objection was clearly noted, but not accepted. Other suggestions you had in the recent past were more fruitful. I suggest we shake out of this local minimum because it seems we're stuck.