Bonferroni Inequalities
المؤلف:
Dohmen, K.
المصدر:
Improved Bonferroni Inequalities with Applications: Inequalities and Identities of Inclusion-Exclusion Type. Berlin: Springer-Verlag, 2003.
الجزء والصفحة:
...
7-3-2021
1939
Bonferroni Inequalities
Let 
be the probability that 
is true, and 
be the probability that at least one of 
, 
, ..., 
is true. Then "the" Bonferroni inequality, also known as Boole's inequality, states that
where 
denotes the union. If 
and 
are disjoint sets for all 
and 
, then the inequality becomes an equality. A beautiful theorem that expresses the exact relationship between the probability of unions and probabilities of individual events is known as the inclusion-exclusion principle.
A slightly wider class of inequalities are also known as "Bonferroni inequalities."
REFERENCES:
Comtet, L. "Bonferroni Inequalities." §4.7 in Advanced Combinatorics: The Art of Finite and Infinite Expansions, rev. enl. ed. Dordrecht, Netherlands: Reidel, pp. 193-194, 1974.
Dohmen, K. Improved Bonferroni Inequalities with Applications: Inequalities and Identities of Inclusion-Exclusion Type. Berlin: Springer-Verlag, 2003.
Galambos, J. and Simonelli, I. Bonferroni-Type Inequalities with Applications. New York: Springer-Verlag, 1996.
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