The Annals of Probability
- Ann. Probab.
- Volume 14, Number 4 (1986), 1391-1398.
Compound Poisson Approximations for Sums of Random Variables
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.
Ann. Probab., Volume 14, Number 4 (1986), 1391-1398.
First available in Project Euclid: 19 April 2007
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Serfozo, Richard F. Compound Poisson Approximations for Sums of Random Variables. Ann. Probab. 14 (1986), no. 4, 1391--1398. doi:10.1214/aop/1176992379. https://projecteuclid.org/euclid.aop/1176992379
- See Correction: Richard F. Serfozo. Correction: Compound Poisson Approximations for Sums of Random Variables. Ann. Probab., Volume 16, Number 1 (1988), 429--430.