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Compound Poisson approximations for sums of random variables. (English) Zbl 0604.60016
We show that a sum of dependent random variables is approximately compound Poisson when the variables are rarely nonzero and, given they are nonzero, their conditional distributions are nearly identical. We give several upper bounds on the total-variation distance between the distribution of such a sum and a compound Poisson distribution. Included is an example for Markovian occurrences of a rare event. Our bounds are consistent with those that are known for Poisson approximations for sums of uniformly small random variables.

MSC:
60E15 Inequalities; stochastic orderings
60F99 Limit theorems in probability theory
60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
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