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

Janos Galambos and Italo Simonelli

Statistics & Probability Letters, 1996, vol. 28, issue 2, 147-151

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

Keywords: At; least; r; events; out; of; n; occurring; Binomial; moments; Bonferroni-type; inequalities; Reduction; to; independent; events; Reduction; to; Bonferroni; bounds; of; no; occurrences (search for similar items in EconPapers)
Date: 1996
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Citations: View citations in EconPapers (1)

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