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Suppose you have a bunch of independent time series each with binary outcomes A/B, all with the same CDF (but we don't know anything about it a-priori). We want to compute the average percentage of A outcomes, or better yet, the empirical CDF. The problem is that we only have information when the A outcome occurs. So if one time series has the following outcomes : B, B, B, A we are only informed when A occurs and when it does we know that 3 Bs occurred since the start / last A outcome.

Our naïve way of doing right now is to compute the percentage of A outcomes every time information is given, but my hunch is that the "delayed" information must bias that percentage.

Can someone point me in the right direction towards getting a statistically correct answer?

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Are you saying that there are actually 3 possible outcomes, A, B, or neither? Otherwise why can't you tell that B occurred given that A did not? – gung Oct 15 '12 at 19:09

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If you data is that you get a series of 0 or more B's then an A and the collection of the data stops there (then you get latter independent sequences), then you could model this with a geometric distribution (or more generally a negative binomial if you stop on the k'th A).

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