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Poisson approximation for large deviations
205
Citations
3
References
1990
Year
Large DeviationsEngineeringMathematical StatisticRandom GraphUncertainty QuantificationStructural Graph TheoryDiscrete MathematicsIndicator VariablesProbabilistic Graph TheoryApproximation TheoryStatisticsAbstract UpperProbability TheoryPoisson ApproximationConstructive ApproximationGraph TheoryApproximation MethodExtremal Graph TheoryLower Bounds
Abstract 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.
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