Bivariate Binomial Moments and Bonferroni-Type Inequalities |
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Authors: | Qin Ding Eugene Seneta |
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Institution: | 1.School of Mathematics and Statistics,FO7, University of Sydney,Sydney,Australia |
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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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