Bivariate Binomial Moments and Bonferroni-type Inequalities

2015/11/20 by Ding, Qin, Seneta, Eugene
#60C05(Secondary) #60E05 (Primary) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1511.06640

Abstract

We obtain bivariate forms of Gumbel's, Fréchet's and Chung's linear inequalities for P(S≥ u, T≥ v) in terms of the bivariate binomial moments \S_i,j\, 1≤ i≤ k, 1≤ j≤ l of the joint distribution of (S,T). At u=v=1, the Gumbel and Fréchet bounds improve monotonically with non-decreasing (k,l). The method of proof uses combinatorial identities, and reveals a multiplicative structure before taking expectation over sample points.

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