3 ms·
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
by shiandow 2y ago
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.
- tmoertel 2y agoAnother 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.html https://blog.moertel.com/posts/2024-08-23-sampling-with-sql....
- foldU 2y ago(author of OP) That post of yours was actually what got me tooling around with this stuff again :) it's a really excellent one
- tmoertel 2y agoThanks! 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.
- gmfawcett 2y agoNice article!