A Note on the Bonferroni's Inequalities

In this note we present improved Bonferroni type inequalities for the union of a set of nonexchangeable events. These new bounds are stronger than or equivalent with the bounds proposed by KOUNIAS (1968), HUNTER (1976), MARGOLIN & MAURER (1976), GALAMBOS (1977) and by Mǎrgǎkritescu (1983). In the particular case of the exchangeable events, the bounds given by SOBEL & UPPULURI (1972) can be derived. A generalization in terms of a partition of {1, 2, …, n } is also established.