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!



Parameter estimation distribution for hypergeometric distribution
You can use maximum likelihood estimation:
<https://en.m.wikipedia.org/wiki/Maximum_likelihood_estimation>


