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Let the hypergeometric distribution is given by $h(k\mid N;M;n)$, where

  • $k$ is the number of observed successes,
  • $N$ is the population size,
  • $M$ is the number of success states in the population and
  • $n$ is the number of draws.

Now if I know $N$ and $n$ and have $k$ successes, I would like to estimate the number $M$. Of course, I could estimate it with $kN/n$. However, I would like to assign the probability distribution for all numbers between $k$ and $N-(n-k)$, that it is the number $M$.

Many thanks for your help in advance!

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You can use maximum likelihood estimation: https://en.m.wikipedia.org/wiki/Maximum_likelihood_estimation

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  • $\begingroup$ Many thanks for your input. But if I have to assign a probability to each natural number, like saying the probability that $a$ is the value $M$ is $p(a)$, how would I do that? This is probably a very simple question, but I am insecure how to derive that from the maximum likelihood estimation. $\endgroup$ – tobias Nov 10 '16 at 15:21
  • $\begingroup$ The standard answer is that you can't have probabilities here, instead you have to work with likelihoods. $\endgroup$ – Bjørn Kjos-Hanssen Nov 10 '16 at 16:55

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