ESAIM Probability and Statistics · 1999 · 95 citations · 7 references
Natural SciencesMathematicsProbability TheoryStatisticsStochastic ProcessesPerturbation MethodsPerturbation TheoryPoisson ProcessesProbability DistributionsCompound Poisson DistributionsCompound Poisson ModelsCompound Poisson ProcessesDependent VariablesIndependent VariablesPoisson Random MeasuresProbability Inequalities For Sums Of Random Variables
Stein's method is used to prove approximations in total variation to the distributions of integer valued random variables by (possibly signed) compound Poisson measures. For sums of independent random variables, the results obtained are very explicit, and improve upon earlier work of Kruopis (1983) and Čekanavičius (1997); coupling methods are used to derive concrete expressions for the error bounds. An example is given to illustrate the potential for application to sums of dependent random variables.
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Poisson Approximation and the Chen-Stein Method
Richard Arratia, Larry Goldstein, Louis Gordon · Statistical Science · 1990 · 351 citations · Full text