Why person-years follow a Poisson ditribution? While studing poisson distributions, this simple question came to my mind:
Poisson distribution are made of variables which only have integer numbers and are always >0 (as an example: number of myocardial infarction in an hospital).
It is usually said that this variable still follow a poisson distribution when taking into account the follow-up period by the person-years unit, instead of just number of events, but why? Aren't person-years units non-integer, since the can also have values of, as an example, 0.8 or 2.5?
Example: https://www.statsdirect.com/help/rates/poisson_rate_ci.htm

I think it boils down to that, following your example, a count of 14 events over 400 person-years, gives a Poisson rate parameter estimate of 0.35 events per person-year. So if you were to track one person over a year, you'd have a 70% chance of observing no events, 25% of one event, 4% of two events, & so on; on average 0.35 events, but no non-integer counts.
It's a consequence of the memorylessness of the Poisson process & that the sum of independent Poisson random variables is a Poisson r.v. with a rate equal to the sum of their individual rates.
