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A generator for explicit univariate lower bounds

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  • Seneta, Eugene
  • Chen, John T.

Abstract

This note applies the method of indicator functions to derive a general inequality for the probability that at least one out of n events occurs. The result is in the spirit of the early work of [Chung, 1941,1943, Ann. Math. Statist. 12, 328-338; Ann. Math. Statist. 14, 123-133] and [Rényi, 1958, J. de Mathematique 37, 393-398] on general bounds using Borel functions of Bonferroni summations. This general method can be used to derive inequalities of specific forms. In particular, we use the proposed general method to re-derive the celebrated Dawson-Sankoff degree-two lower bound; develop a degree-three bound that is complementary in structure to the Sobel-Uppuluri-Galambos (degree-three) lower bound; and obtain a degree-three lower bound similar in structure to the Dawson-Sankoff bound. Numerical examples to illustrate are included.

Suggested Citation

  • Seneta, Eugene & Chen, John T., 2005. "A generator for explicit univariate lower bounds," Statistics & Probability Letters, Elsevier, vol. 75(4), pages 256-266, December.
    • Handle: RePEc:eee:stapro:v:75:y:2005:i:4:p:256-266
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    References listed on IDEAS

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    1. Chen, Jie & Glaz, Joseph, 2002. "Approximations for a conditional two-dimensional scan statistic," Statistics & Probability Letters, Elsevier, vol. 58(3), pages 287-296, July.
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