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October, 1986 Compound Poisson Approximations for Sums of Random Variables
Richard F. Serfozo
Ann. Probab. 14(4): 1391-1398 (October, 1986). DOI: 10.1214/aop/1176992379

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.

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Richard F. Serfozo. "Compound Poisson Approximations for Sums of Random Variables." Ann. Probab. 14 (4) 1391 - 1398, October, 1986. https://doi.org/10.1214/aop/1176992379

Information

Published: October, 1986
First available in Project Euclid: 19 April 2007

zbMATH: 0604.60016
MathSciNet: MR866359
Digital Object Identifier: 10.1214/aop/1176992379

Subjects:
Primary: 60E15
Secondary: 60F99 , 60J10

Keywords: compound Poisson distribution , rare Markovian events , sums of dependent variables , total variation distance

Rights: Copyright © 1986 Institute of Mathematical Statistics

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Vol.14 • No. 4 • October, 1986
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