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An extension of the method of polynomials and a new reduction formula for Bonferroni-type inequalities

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  • Galambos, Janos
  • Simonelli, Italo

Abstract

We prove that Bonferroni-type inequalities on the probability of at least r events occurring out of n are valid if, and only if, they are valid for a triangular array of independent events. Such method for proof was so far available for the case of exactly r events occurring. This new method allows us to reduce the mentioned Bonferroni-type inequalities to the special case of none occurring. This reduction method is exploited to establish a large class of new inequalities

Suggested Citation

  • Galambos, Janos & Simonelli, Italo, 1996. "An extension of the method of polynomials and a new reduction formula for Bonferroni-type inequalities," Statistics & Probability Letters, Elsevier, vol. 28(2), pages 147-151, June.
    • Handle: RePEc:eee:stapro:v:28:y:1996:i:2:p:147-151
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    Cited by:

    1. Simonelli, Italo, 1999. "An Extension of the Bivariate Method of Polynomials and a Reduction Formula for Bonferroni-Type Inequalities," Journal of Multivariate Analysis, Elsevier, vol. 69(1), pages 1-9, April.

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