Empirical Bayes rules for selecting the most and least probable multivariate hypergeometric event

In this paper, we consider a multivariate hypergeometric population with k-category π = π(N, M, s1,…,sk), where si, i = 1,…,k, is the number of units in category πi, with Σi−1k si = M, the total number of units in population π, and N is the number of units selected from population π. Let s[1] = min1⩽i⩽k si, s[k] = max1⩽i⩽k si. A category associated with si = s[k] (or si = s[1]) is considered as the most (or the least) probable event. We are …