Do there exist any statistical methods for estimating population size? I’m thinking of, say, an advertiser who wants to verify a magazine’s claim to have a gazillion subscribers.

Obviously you can count the subscriptions (discounting fraud) but does there exist any method for estimating population? Sort of the reverse of the usual statistical process of extracting information from a known population.

If the subscriptions are numbered consecutively and you can get a random sample, you can estimate the number of subscriptions. This is what’s known as the German tank problem, after a particularly pressing instance back in the early '40s.

Edit: You could also take a poll to estimate what proportion of a given demographic are subscribers. You can then multiply that by the size of the demographic to estimate the size of the subscriber base within that demographic. That’s probably easier if this is a real problem, as it doesn’t involve getting proprietary information from the magazine.