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

Author

Listed:
  • John T. Chen

    (Bowling Green State University)

  • Eugene Seneta

    (University of Sydney)

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.

Suggested Citation

  • John T. Chen & Eugene Seneta, 2006. "A Fréchet-Optimal Strengthening of the Dawson-Sankoff Lower Bound," Methodology and Computing in Applied Probability, Springer, vol. 8(2), pages 255-264, June.
    • Handle: RePEc:spr:metcap:v:8:y:2006:i:2:d:10.1007_s11009-006-8551-z
    DOI: 10.1007/s11009-006-8551-z
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    References listed on IDEAS

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    1. Hoppe, Fred M., 1985. "Iterating bonferroni bounds," Statistics & Probability Letters, Elsevier, vol. 3(3), pages 121-125, June.
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