Compound Poisson approximations for sums of random variables (Q5903578)

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.