Comment by shiandow | Hacker News Reader

Comment by shiandow | Hacker News Reader

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Poisson processes are neat, they always end up working nicely in ways that many other distributions/processes very much don't.

Splitting a Poisson process into two lower rate processes is a neat trick. Even better is that you can do the same to convert a Poisson process into one with a variable rate, provided that rate is lower than the original (original may be variable as well).

And the fact that the partial sums of a bunch of exponential distributions results in the same distribution of values as picking Poisson(lambda * time) values uniformly at random is pure magic.

Another neat property of Poisson processes is that when raced against one another, they win in proportion to their underlying rates. This property is the basis of a clever random sampling algorithm that works well in SQL:

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

For an explanation of how it works, see https://blog.moertel.com/posts/2024-08-23-sampling-with-sql....

(author of OP) That post of yours was actually what got me tooling around with this stuff again :) it's a really excellent one

Thanks! That was very kind of you to say. Whenever I write stuff like that, I wonder, "Does anyone find this useful?" It helps to hear every once in a while that the answer is sometimes yes.

Nice article!

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