1977/08/01 by János Galambos · 1 citation
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #Binomial (polynomial) #Bonferroni correction #Combinatorics #Discrete mathematics #Extension (predicate logic) #Limits and Structures in Graph Theory #Markov Chains and Monte Carlo Methods #Mathematical analysis #Mathematics #Moment (physics) #Statistics #Upper and lower bounds
paper · pdf · doi:10.1214/aop/1176995765
openalex publication_date 1977/08/01 · openalex created_date 2025/10/10 · openalex updated_date 2025/11/06
Let A1, A2, ⋯, An be events on a probability space. Let Sk,n be the kth binomial moment of the number mn of those A's which occur. An estimate on the distribution yt = P(mn \geqq t) by a linear combination of S1,n, S2,n, ⋯, Sn,n is called a Bonferroni inequality. We present for proving Bonferroni inequalities a method which makes use of the following two facts: the sequence yt is decreasing and Sk,n is a linear combination of the yt. By this method, we significantly simplify a recent proof for the sharpest possible lower bound on y1 in terms of S1,n and S2,n. In addition, we obtain an extension of known bounds on yt in the spirit of a recent extension of the method of inclusion and exclusion.