> Poisson is such an under-utilized distribution for these kinds of phenomena.

Yeah, Poisson distributions show up everywhere if you are paying attention. You can even use the theory as the basis for a fast, elegant algorithm to take parallel, weighted random samples. You can even do it in SQL!:

    SELECT *
    FROM Population
    WHERE weight > 0
    ORDER BY -LN(1.0 - RANDOM()) / weight
    LIMIT 100  -- Sample size.

For more on the Poission connection, see: https://blog.moertel.com/posts/2024-08-23-sampling-with-sql....

Isn't it a natural modeling choice? If your events arrive on exponentially distributed deltas, you end up having poisson arrival counts.

possion distribution is what i learned in university for describing this kind of event?

the book is underutilized?

No I learned it in university like most of us did but 10+ years in tech I have never once seen somebody reach out for it in situations like this one where it is a natural fit.

Few people understand it well, even though it's effectively a binomial distribution (easy to grok) but with special constraints.