Compound Poisson Approximations for Sums of Random Variables

Other literature type English OPEN
Serfozo, Richard F. (1986)
  • Publisher: The Institute of Mathematical Statistics
  • Journal: (issn: 0091-1798)
  • Related identifiers: doi: 10.1214/aop/1176992379
  • Subject: Compound Poisson distribution | total variation distance | sums of dependent variables | rare Markovian events | 60E15 | 60F99 | 60J10

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.
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