Here, the important parameters I used were:

- average investment in bitcoin is $1000 (buy outright, or mining equipment)

- estimated the percentage of holders whether they had invested at $100, $10, $1, $0.1 or $0.01

- Ones invested at $100/BTC still have their whole investment, others have sold 20%, 40%, 60% or 80%, respectively.

- Calculate weighted average, how much is the present value of an average remaining bitcoin investment (=$3,400, which is quite small for the reason that 80% were estimated to have bought in at about $100)

- Divide bitcoin market cap by the previous figure, obtaining number of holders (700,000).

- arrange the number of people in a certain log-bracket so that they approximately conform to bell curve (found out in other similar data that thy do) and satisfy the constraints of total bitcoins and the known stash of Satoshi and some idea of the top-heaviness of the distribution. <= it is essentially a parameter, how many coins to allocate to BTC10,000+ bracket. I think the realistic range is BTC3M to BTC7M, including Satoshi's 1M.

- almost nothing in the distribution changes if the number of holders is 200k instead of 600-700k. The bulk of the bitcoins is held by the top, and their number is inversely correlated to their average holding. The average holding must follow certain rules so there are not many parameters.

edit: Ah, as I was writing, I remembered that average remaining investment was calculated with bitcoin price of $100 instead of the current $200. This makes the total number of bitcoin users 350,000, which I think is very realistic considering other metrics.