Number of samples that were taken to have observed a specific s

The Inverse Hypergeometric distribution was derived in the previous topic as a distribution of variability, in predicting the number of failures one will have before the sth success. However, it can equally be derived as a distribution of uncertainty about the number of failures x = n - s one must have had if one knows s, M, D using Bayes' Theorem and a Uniform (i.e. uninformed) prior on x. So:

n = s + VoseInvHypergeo(s,D,M)