Bonferroni bounds revisited

1989 ◽  
Vol 26 (2) ◽  
pp. 233-241 ◽  
Author(s):  
Stratis Kounias ◽  
Kiki Sotirakoglou
Keyword(s):  
Normal Distribution ◽  
Multivariate Normal Distribution ◽  
Upper Bounds ◽  
Multivariate Normal ◽  
Lower And Upper Bounds

Lower and upper bounds of degree m for the probability of the union of n not necessarily exchangeable events are established. These bounds may be constructed to improve the Bonferroni and the Sobel–Uppuluri bounds.An application to equi-correlated multivariate normal distribution is given.

Bonferroni bounds revisited

1989 ◽  
Vol 26 (02) ◽  
pp. 233-241 ◽  
Author(s):  
Stratis Kounias ◽  
Kiki Sotirakoglou
Keyword(s):  
Normal Distribution ◽  
Multivariate Normal Distribution ◽  
Upper Bounds ◽  
Multivariate Normal ◽  
Lower And Upper Bounds

Lower and upper bounds of degree m for the probability of the union of n not necessarily exchangeable events are established. These bounds may be constructed to improve the Bonferroni and the Sobel–Uppuluri bounds. An application to equi-correlated multivariate normal distribution is given.

Upper bounds for the probability of a union by multitrees

2001 ◽  
Vol 33 (2) ◽  
pp. 437-452 ◽  
Author(s):  
József Bukszár
Keyword(s):  
Graph Theory ◽  
Normal Distribution ◽  
Multivariate Normal Distribution ◽  
Upper Bounds ◽  
Distribution Functions ◽  
Multivariate Normal ◽  
Common Generalization

The problem of finding bounds for P(A1 ∪ ⋯ ∪ An) based on P(Ak1 ∩ ⋯ ∩ Aki) (1 ≤ k1 < ⋯ < ki ≤ n, i = 1,…,d) goes back to Boole (1854), (1868) and Bonferroni (1937). In this paper upper bounds are presented using methods in graph theory. The main theorem is a common generalization of the earlier results of Hunter, Worsley and recent results of Prékopa and the author. Algorithms are given to compute bounds. Examples for bounding values of multivariate normal distribution functions are presented.

Sign in / Sign up

Export Citation Format

Share Document