Bonferroni Inequalities

Bonferroni-Galambos Inequalities for Partition Lattices

In this paper, we establish a new analogue of the classical Bonferroni inequalities and their improvements by Galambos for sums of type ∑ π∈P(U)(−1)(|π| − 1)!f(π) where U is a finite set, P(U) is the partition lattice of U and f : P(U) → R is some suitable non-negative function. Applications of this new analogue are given to counting connected k-uniform hypergraphs, network reliability, and cum...

Bonferroni-type inequalities and binomially bounded functions

We present a unified approach to an important subclass of Bonferroni-type inequalities by considering so-called binomially bounded functions. Our main result associates with each binomially bounded function a Bonferroni-type inequality. By appropriately choosing this function, several well-known and new results are deduced.

Support Approximations Using Bonferroni-Type Inequalities

Improved Bonferroni Inequalities via Abstract Tubes - ReadingSample

1 Introduction and Overview Many problems in combinatorics, number theory, probability theory, reliability theory and statistics can be solved by applying a unifying method, which is known as the principle of inclusion-exclusion. The principle of inclusion-exclusion expresses the indicator function of a union of finitely many sets as an alternating sum of indicator functions of their intersecti...

Upper Bounds for Bivariate Bonferroni-type Inequalities Using Consecutive Events

Let A1, A2, . . . , Am and B1, B2, . . . , Bn be two sequences of events on the same probability space. Let X = Xm(A) and Y = Yn(B), respectively, denote the numbers of those Ai’s and Bj ’s which occur. We establish new bivariate Bonferroni-type inequalities using consecutive events and deduce a known result.