The Annals of Probability

Compound Poisson Approximations for Sums of Random Variables

Richard F. Serfozo

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Abstract

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.

Article information

Source
Ann. Probab., Volume 14, Number 4 (1986), 1391-1398.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176992379

Digital Object Identifier
doi:10.1214/aop/1176992379

Mathematical Reviews number (MathSciNet)
MR866359

Zentralblatt MATH identifier
0604.60016

JSTOR
links.jstor.org

Subjects
Primary: 60E15: Inequalities; stochastic orderings
Secondary: 60F99: None of the above, but in this section 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)

Keywords
Compound Poisson distribution total variation distance sums of dependent variables rare Markovian events

Citation

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


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Corrections

  • See Correction: Richard F. Serfozo. Correction: Compound Poisson Approximations for Sums of Random Variables. Ann. Probab., Volume 16, Number 1 (1988), 429--430.