Bonferroni-type inequalities via interpolating polynomials

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...

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

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.

BONFERRONI-TYPE INEQUALITIES; CHEBYSHEV-TYPE INEQUALITIES FOR THE DISTRIBUTIONS ON [0, n]

Abs t rac t . An elementary "majorant-minorant method" to construct the most stringent Bonferroni-type inequalities is presented. These are essentially Chebyshev-type inequalities for discrete probability distributions on the set {0, 1 , . . . , n}, where n is the number of concerned events, and polynomials with specific properties on the set lead to the inequalities. All the known resuits are ...