You might consider submitting some of this to the Wolfram Function Repository. The individual functions are a good fit for that site. And it has already several distributions, e.g. NonNegativeExcessDistribution, which means there are in effect templates one might follow for adding new ones.
Some functions from the WFR get migrated to the system. Not my call whether this one would. But if you want it to be made generally available, the WFR is the best place unless and until it gets adapted into the Wolfram Language.
I am trying to submit to WFR, but its CodeInspect doesn't like the code which has worked for 13 years. I have requested help from the WFR team, I'll let you know if it ever gets accepted,
