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My data is something like this:

I have U urns, and I have taken a bag of $n$ objects from each urn. Each urn has $N$ objects, and I have sampled $n$ with replacement.

$n$ is comprised of coloured balls (e.g. $m_1$ blue balls, $m_2$ green balls, $m_3$ yellow balls... Etc., And $\sum_j m_j = n$). Bear in mind that each $m_1, m_2...$ is small and $j \rightarrow \infty$.

What would be a distribution that can be used to describe the probability of sampling 1 blue ball in two (or more) different bags in this scenario?

Anonymous Scientist
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  • See https://stats.stackexchange.com/questions/5347 for instance. For more, search our site for questions about the [Poisson-Binomial distribution](https://stats.stackexchange.com/search?tab=votes&q=%22poisson%20binomial%22) – whuber Jun 14 '20 at 16:18
  • Thank you so much! I'll give this a look and see how it aligns with my use case. One more thing I'd also like to model is the overlap between the urns in my scenario, and trying to estimate the number of urns. Would a Poisson binomial also be relevant here? – Anonymous Scientist Jun 21 '20 at 08:02
  • It depends on what you mean by "overlap between the urns." Usually it's better here on CV to describe your actual use case (rather than attempting to abstract your question, which often leaves out crucial details). – whuber Jun 21 '20 at 13:16

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