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!


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

  • $\begingroup$ 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

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.