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Compound Poisson approximations for sums of random variables. (English) Zbl 0638.60052
We show that a sum of dependent random elements taking values in a semigroup is approximately compound Poisson when the elements 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.
Reviewer: R.F.Serfozo

60F99 Limit theorems in probability theory
60G99 Stochastic processes
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