 A generator for explicit univariate lower boundsEugene Seneta and John T. Chen Statistics & Probability Letters, 2005, vol. 75, issue 4, 256-266 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. Keywords: Probability; inequality; Borel; function; Bonferroni; summations (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:stapro:v:75:y:2005:i:4:p:256-266 Ordering information: This journal article can be ordered from Access Statistics for this article Statistics & Probability Letters is currently edited by Somnath Datta and Hira L. Koul More articles in Statistics & Probability Letters from Elsevier |
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