Premium
A Note on the Bonferroni's Inequalities
Author(s) -
Mǎrgǎritescu E.
Publication year - 1986
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.4710280807
Subject(s) - bonferroni correction , mathematics , generalization , partition (number theory) , sobel operator , inequality , combinatorics , set (abstract data type) , statistics , mathematical economics , mathematical analysis , computer science , artificial intelligence , edge detection , image (mathematics) , programming language , image processing
Abstract In this note we present improved Bonferroni type inequalities for the union of a set of nonexchangeable events. These new bounds are stronger than or equivalent with the bounds proposed by KOUNIAS (1968), HUNTER (1976), MARGOLIN & MAURER (1976), GALAMBOS (1977) and by Mǎrgǎkritescu (1983). In the particular case of the exchangeable events, the bounds given by SOBEL & UPPULURI (1972) can be derived. A generalization in terms of a partition of {1, 2, …, n } is also established.