On Mon, 1 Oct 2018 at 15:04, Hans Dembinski via Boost
Poisson is correct, for example, when you monitor a random process for a while which produces some value x at random points in time with a constant rate. You bin the outcomes, and then stop monitoring at an arbitrary point in time. This is the right way to model many physics experiments. It is also correct if you make a survey with a random number of participants, i.e. when you pass the survey to a large number of people without knowing beforehand how many are going to respond.
Multinomial is correct, when there is a predefined fixed number of events, each with a random exclusive outcome, and you bin those outcomes. The important point is that the number of events is fixed before the experiment is conducted. This is the main difference to the previous case, where the total of events is not known beforehand. This would be correct, if you make a survey with a fixed number of participants, which you invite explicitly and don't start the analysis before all have return the survey.
From what you are saying, and I have no knowledge at all in this matter [just reading what you say], it seems that a policy approach, to allow for both distributions, seems appropriate. Don't want to give you more work, but you just made the [that] point yourself.
degski -- *“If something cannot go on forever, it will stop" - Herbert Stein*