Document poisson-binomial distribution

[WardBrian]

Submission Checklist

• Builds locally
• New functions marked with <<{ since VERSION }>>
• Declare copyright holder and open-source license: see below

Summary

Documentation for stan-dev/stanc3#1690

Copyright and Licensing

Please list the copyright holder for the work you are submitting (this will be you or your assignee, such as a university or company):
Simons Foundation

By submitting this pull request, the copyright holder is agreeing to license the submitted work under the following licenses:

• Code: BSD 3-clause (https://opensource.org/licenses/BSD-3-Clause)
• Documentation: CC BY-ND 4.0 (https://creativecommons.org/licenses/by-nd/4.0/)

[bob-carpenter]

Thanks, this looks great. I hadn't realized this was added. Just a couple clarifications requested in the doc and the notation.

[WardBrian]

I hadn't realized this was added

It had a long journey. Original math implementation was in 2020, it had some issues until 2025, and then slipped through the cracks of actually being exposed in the language until I did a sweep through old issues this week