Given I have a set of values N, where N is unknown to me. I can make requests for one sample at a time, which is selected randomly for me. As I request more samples, I see more and more values which I have seen before, and new values become more rare. How many do I need to request before I can be 95% confident that I know what N is?
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3Is there an ordering to the items, ie, the german tank problem, or are we just estimating the size of an unknown population? – Andrew M Apr 12 '16 at 17:44
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3Is $N$ a finite set of distinct values? If so, this is the famous coupon collectors problem, see for instance http://stats.stackexchange.com/questions/87494/estimating-n-in-coupon-collectors-problem – kjetil b halvorsen Apr 12 '16 at 17:45
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"How many do I need to request before I can be 95% confident that I know what N is?" I take it by this you mean you are 95% confident that it is a particular value, rather than that you are taking a 95% confidence interval? – Silverfish Apr 12 '16 at 18:05
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There is no ordering, there are N distinct values, but I don't know what N is. It does appear to be the variation of the coupon collectors problem named the fortune cookie message problem. In my specific case, I'm trying to gather the names of a servers behind a load balancer, which I am assuming randomly chooses servers for my requests. – Tom Cooper Apr 13 '16 at 15:39
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This is indeed the fortune cookie message problem as described here. Thanks to kjetil for pointing me in that direction!
