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!