## Estimate userbase size based on existence of usernames of varying popularity [closed]

Suppose you have three sets of data.

One is a set of site names mapped to number of users

Ex.:

hotmail,1500000
yahoo,10000000


Second is a set of usernames, ex.:

starbaby
lucifer


Third is a set of username:site pairs, signifying the username from the set above exists in the set of that site's users e.g.

starbaby,hotmail
starbaby,yahoo
lucifer,yahoo


How can you estimate the number of users of a novel site not in the first set based on the existence/non-existence of each of the usernames in the username set for that site?

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-1: This seems like it should go to stackoverflow if anywhere, it really doesn't seems "Research Mathematics" level and I'm relatively sure this problem is unsolvable, because of a dearth of information and because you don't know anything about the distribution of people in each of the sites and any connections between the sites. (messed up and posted this as an answer, deleting it) – Michael Hoffman Jun 24 2010 at 22:41
There may be an interesting problem in there, but right now it's not clear to me what it is. If you have the username set for the site, can't you estimate the number of users by counting the number of usernames? I'd like to close this as "needs revision", but that's not one of the options, so I'll go with "not a real question". If you edit the question so that it's clearer what the problem is (and it turns out to be a mathematics problem rather than, say, a human psychology problem), the question can be reopened. – Anton Geraschenko Jun 25 2010 at 6:39
The closure as "not a real question" seems rash. The particular content of Michael Hoffman's comments seem like a reason not to repose confidence in his judgment. Maybe "needs revision" is appropriate. I'd encourage the poster to post a revised version. – Michael Hardy Jun 25 2010 at 20:53
@Michael Hardy: Sorry, I guess I wasn't very clear. If it were available, I would have voted to close as "needs revision". The reason I decided that "not a real question" is the most appropriate available reason is that the asker has not made it clear what the question is and what the available data are. If the question is revised (please edit, do not repost), then I'm happy to reopen it. Specifically, the revised version should make it clear why "count the number of usernames" is not a solution to the problem. My reasoning for closing made no reference to Michael Hoffman's comment. – Anton Geraschenko Jun 25 2010 at 22:44
If the question means what I think it means, then "count the number of users" would not answer the question because none of the lists of users is complete. – Michael Hardy Jun 27 2010 at 0:10