For the particular case of the exponential distribution we can go further. By taking advantage of the theory of Poisson processes, we can take samples using a parallel algorithm. It even has a surprisingly succinct SQL translation:
SELECT *
FROM Population
WHERE weight > 0
ORDER BY -LN(1.0 - RANDOM()) / weight
LIMIT 100 -- Sample size.
If you're curious, I explore this algorithm and the theory behind it in https://blog.moertel.com/posts/2024-08-23-sampling-with-sql....
Quite off-topic, but do you know when you'll write the article about CPS, if ever?
Oops. I had quite forgotten that I need to write about that. I said I would over a decade ago, so that's a long time for you to wait. Sorry about that.
I mainly write for myself, so I need the time and the motivation. Until recently, my job at G took up my time and also provided an internal community where I could scratch the writing itch, which reduced the motivation for public writing on my blog. But now that I'm semi-retired, I'll try to write more frequently.
Thanks for the accountability!
Inverse transform sampling is a special case of normalizing flow where we don't need to learn anythin.g
Sampling from a standard uniform distribution and then using the inverse transform is the commonest way of generating random numbers from an arbitrary distribution.
0. https://en.m.wikipedia.org/wiki/Inverse_transform_sampling
1. https://en.m.wikipedia.org/wiki/Probability_integral_transfo...
2. Not every cdf is one-to-one, however, so you may need a generalized inverse.