You could attempt to replicate the analysis used in "Quantitative Analysis of the Full Bitcoin Transaction Graph" by Dorit Ron and Adi Shamir. (
http://eprint.iacr.org/2012/584.pdf)
In 2012 they noted that:
“If we sum up the amounts accumulated at the 609,270 addresses which only receive and never send any BTC’s [bitcoins], we see that they contain 7,019,100 BTC’s, which are almost 78% of all existing BTC’s. Due to the way bitcoins can be repeatedly moved to fresh addresses, some of which can be very recent, we can not claim that all these bitcoins are out of circulation. However,76.5% of these 78% (i.e., 59.7% of all the coins in the system) are old coins", de ned as bitcoins received at some address more than three months before the cut off date (May 13th 2012), which were not followed by any outgoing transac-
tions from that address after they were received. One can also argue that very old dormant bitcoins were simply abandoned or lost by users who experimented with the system in its early days, when it was very dicult to buy anything or to exchange bitcoins into dollars. To be even more cautious with our estimation of dormant bitcoins, we decided to ignore all the transactions which took place prior to July 18th 2010, when Mt.Gox started its exchange and price quoting services. The sum of the balances of all the addresses which have not been
active since that date is 1,657,480 bitcoins. Clearly, by considering all these bitcoins as "lost" rather than "hoarded" we are underestimating the number of bitcoins which are kept dormant in "saving accounts". By ignoring these very old bitcoins and repeating the same calculation, we found that 73% of all the remaining BTC's were accumulated at addresses which only receive and never send bitcoins, and that 70% of these 73% (i.e., 51%) are dormant bitcoins in the sense that they were received more than three months before our cuto date but
after it became easy to exchange them. If instead of summing the transaction values we sum the nal balances of all the addresses that were active after July 18th 2010 but became inactive in the last three months, we get that 55% of all
coins in the system are dormant in this sense. This is strong evidence that the majority of bitcoins are not circulating in the system, and since it is based on the address rather than the entity graph, this conclusion is not a ected by possible
inaccuracies in the way we associate addresses with users.”