Some optimal bivariate Bonferroni-type bounds

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.

Binary segmentation and Bonferroni-type bounds

−∞ φ(t− ξ) · Φ(νt) dt, where φ and Φ are the pdf and cdf of N(0, 1), respectively. We derive two recurrence formulas for the effective computation of its values. We show that with an algorithm for this function, we can efficiently compute the second-order terms of Bonferroni-type inequalities yielding the upper and lower bounds for the distribution of a max-type binary segmentation statistic in...

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

Error bounds for bivariate piecewise hermite interpolation