Why person-years follow a Poisson ditribution?

Question

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

@PeterO. thanks for your answer but, even if there is a clear explanation of how poisson models work, it doesn't actually answer my question (or at least I cannot find a similar example) — Claudio Laudani, Sep 12 '21 at 13:21
It's only a comment, not an answer, and it merely shows a question that may be related to this one. — Peter O., Sep 12 '21 at 13:31

Scortchi - Reinstate Monica · Accepted Answer · 2021-09-12T20:39:42.320

2

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.

edited Sep 12 '21 at 20:39

answered Sep 12 '21 at 20:32

Scortchi - Reinstate Monica

27,560
8
81
248

Thank you very much for your contribution! Hope this could help also other students out there! – Claudio Laudani Sep 12 '21 at 20:34
@ClaudioLaudani: You're welcome – Scortchi - Reinstate Monica Sep 12 '21 at 20:34

Why person-years follow a Poisson ditribution?

1 Answers1