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Improved bivariate Bonferroni-type inequalities

✍ Scribed by Min-Young Lee

Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 258 KB
Volume: 31
Category: Article
ISSN: 0167-7152
DOI: 10.1016/s0167-7152(96)00050-8

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✦ Synopsis

Let A1, A2,...,Am and Bl, B2 ..... B. be two sequences of events on the same probability space. Let Xm and Y,, respectively, be the numbers of those At and Bj which occur. Improved upper bounds and lower bounds of yt,i = P(X~,(A)>>-1, Y.(B)~> 1) in terms of the bivariate binomial moments Sij are obtained, using the method of indicators. We also obtained lower bounds on yij = P(Xm(A) >1 i, Y,(B) >~j).

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