# Parameter estimation distribution for hypergeometric distribution

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 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. – tobias Nov 10 '16 at 15:21