A Fréchet-Optimal Strengthening of the Dawson-Sankoff Lower Bound

John T. Chen () and Eugene Seneta ()
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John T. Chen: Bowling Green State University
Eugene Seneta: University of Sydney

Methodology and Computing in Applied Probability, 2006, vol. 8, issue 2, 255-264

Abstract: Abstract This paper proposes a lower bound for the probability that at least one out of $$n$$ arbitrary events occurs. The information used consists of the first- and second- degree Bonferroni summations in conjunction with $$p_1$$ and $$p_n$$ , where $$p_1$$ is the probability that exactly one event occurs and $$p_n$$ is the probability that all $$n$$ events occur. We prove that the proposed bound is a Fréchet optimal lower bound, which is a criterion difficult to achieve in general. The two additional non-negative terms used in the proposed bound make it at least as good as the Dawson–Sankoff lower bound, a Fréchet optimal degree two lower bound using the first- and second- degree Bonferroni summations only. A numerical example is presented to illustrate that in some cases, the improvement can be substantial.

Keywords: Binomial moments; Fréchet optimality; Dawson–Sankoff inequality; Bonferroni-type bounds; Primary 60E15; Secondary 62P10 (search for similar items in EconPapers)
Date: 2006
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DOI: 10.1007/s11009-006-8551-z

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