So, for a paper I'm writing, I'm using the Poisson probability distribution to compare births per 1,000 people in both Germany and France following World War One. I understand that within the Poisson formula, λ is the average number of events/occurences per time/space. I have a λ chosen from a period during the war, and I wanted to use the Poisson distribution to test the probability of births during the time period of the war reaching a certain metric. Am I able to use this data from during the war as my λ, or do I have to use data before the time period of the war as my λ, and then test this hypothetical value of births against data predating it? I would assume the answer is the latter considering that it seems to make more sense to test probability of a hypothetical based on past events, but I'm not entirely sure.
Thanks for any help.
You should use pre-war birth rates as $\lambda$ and compare it to those during postwar periods.
It wouldn't make sense to use data during the war as that is an obvious "disruption." You should compare two "calm" periods aka before and after the war.