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Poisson approximation for large deviations
Author(s) -
Janson Svante
Publication year - 1990
Publication title -
random structures and algorithms
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.314
H-Index - 69
eISSN - 1098-2418
pISSN - 1042-9832
DOI - 10.1002/rsa.3240010209
Subject(s) - poisson distribution , mathematics , combinatorics , random variable , distribution (mathematics) , statistics , mathematical analysis
Upper and lower bounds are given for P ( S ≤ k ), 0 ≤ k ≤ ES , where S is a sum of indicator variables with a special structure, which appears, for example, in subgraph counts in random graphs. in typical cases, these bounds are close to the corresponding probabilities for a Poisson distribution with the same mean as S . There are no corresponding general bounds for P ( S ≥ k ), k > ES , but some partial results are given.