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: 00911798)

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 totalvariation 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.