Develop a robust battery of statistical tests for our own mathematical functions

[RobertJacobsonCDC]

We implement a few mathematical functions ourselves, in particular:

• sample_single_l_reservoir
• sample_multiple_l_reservoir

These algorithms should have a robust battery of statistical tests ensuring their correctness.

[RobertJacobsonCDC]

#664 adds a few more simple tests for these algorithms.

The intention of this ticket is to create a battery of tests that ensure the statistical correctness of the implementation across a broad range of inputs. We discovered a bug that only manifests when sampling a large-ish number of samples (~100) from a population of thousands, which wasn't caught by our unit tests, as they only sampled 5 items from 100. Since the scientific integrity of models can depend on the correctness of these algorithms, they deserve more mathematical scrutiny than the few tests that currently exist.

The assumptions of the standard Pearson Chi-squared goodness of fit test do not hold: sampling is done without replacement, and thus the samples are not independent. They are "approximately independent," but only for certain inputs. You can experiment with using a Person Chi-squared goodness of fit test (using either our implementation or an "assumed correct" implementation) to see how it "fails" even for correct behavior here:
https://play.rust-lang.org/?version=stable&mode=debug&edition=2024&gist=2d7da2b94f2222219ba00bb15c933cd4

Whether a particular value was ultimately selected in a single sampling run is independent between runs. (The distinction is, sampling inside a single call vs. sampling across calls.) But again, such a test might be feasible only for a a certain range of inputs.

I've written up some more general notes about writing unit tests for statistical functions here.