With no rich list estimating the distribution of Monero is difficult compared to other currencies lacking the privacy properties of Monero.
Are there an published reports of estimated Monero distribution patterns?
If so what are those estimates, and what criteria was used to create them?
Is there enough data to assign a statistical probability to a min/max threshold of the size of the Monero community and the number of wallets over a certain size?
As stated in your question, precision in answering this impossible. The most detailed estimate I have seen is from almost 3 years ago and updated 2 years ago.
Based on the continual growth of all community metrics such as bitcointalk metrics, Reddit subscriptions, network hash rate, node count, transaction data and development activity the userbase has grown by orders of magnitude since 2014.
Assuming a similar distribution to 3 years ago and some partial divestment of some of the largest holders for diversification or other reasons I think possible distribution estimate would be a 20x multiple of Case "A" 2014 estimated users (approximate increase in r/Monero subs between then and indirectly supported by MyMonero account numbers much higher than r/monero subscriptions according to fluffyponyza).
Assuming there are now 20x the 2014 estimated (5,200) we are now looking at about 104,000 users. Only July 20th 2014 when the original estimate was made there were about 2.2 million XMR and today there are about 14.5 million XMR. (14.5/2.2)/20 = a mean XMR holding of around 1/3 the mean size from 2014 (to accommodate a balance between 20x more users and the increase in total XMR supply. This means that although there are many more Monero users now compared to 2014, the additional users (and previous users that have since redistributed some or all of their coins) will now be more heavily weighted towards smaller sized average holdings.
Based on the above, mean XMR holdings may be about 140 coins (total current supply/estimated users) with a very large margin for error. There are likely to be very few "Leviathans" with the great majority of users being "herrings" based on user growth and reasonable redistribution estimates.
Many users never use Reddit or MyMonero and instead rely on the official CLI for which download counts are not recorded. On the other hand some people may have multiple MyMonero or Reddit accounts, making those numbers unreliable as well. Because Monero is so private, we will never know for sure what the exact distribution looks like.
