[WorldMaker]

Disclosure: I am not a subject matter expert, I just do the programming they tell me to do. Mistakes/oversights here are likely my own, not my employer's or the software I work on.

The rain gage analysis the software I work on does is largely based on USGS data. [1] Almost all of that data is publicly accessible and you can explore the data down to individual monitoring stations if you wander through the site far enough.

The application I work with is primarily concerned with two bits of analysis from the data in a given station: average peak annual flow and mean daily flow. The distribution used for analysis of both (beyond linear interpolation and best fit line options) is fitting to a Gamma distribution [2], and plotted on a logarithmic scale. (Rainfall is specifically mentioned under applications of that distribution on Wikipedia, so it seems to be the industry standard even outside of the specific application(s) I work on.)

[1] https://waterdata.usgs.gov/nwis/rt [2] https://en.wikipedia.org/wiki/Gamma_distribution