Multivariate Identities, Permutation and Bonferroni Upper Bounds

We derive identities for the probability that at least a\ and at least ai, and for the probability that exactly a\ and exactly aj, out of n and N events occur (1 < a\ < n, 1 < 02 < N). From this, we produce multivariate permutation hybrid upper bounds, and a multivariate Bonferroni-type upper bound which includes Galambos and Xu's [2] optimal result. The… (More)