publication . Report . Other literature type . Article . 1986

Compound Poisson Approximations for Sums of Random Variables

Richard F. Serfozo;
Open Access
  • Published: 01 Oct 1986
  • Publisher: Defense Technical Information Center
Abstract
Abstract : This document shows 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. It give several upper bounds on the total-variation distance between the distribution of such a sum and a compund Poisson distribution. Included is an example for Markovian occurrences of a rare event. The bounds are consistent with those that are known for Poisson approximations for sums of uniformly small random variables. (Author)
doi: 10.21236/ada158555 , 10.1214/aop/1176992379
Subjects
free text keywords: Compound Poisson distribution, total variation distance, sums of dependent variables, rare Markovian events, 60E15, 60F99, 60J10, Statistics, Probability and Uncertainty, Statistics and Probability, Conditional probability distribution, Random variable, Poisson regression, symbols.namesake, symbols, Applied mathematics, Sum of normally distributed random variables, Zero-inflated model, Mathematics, Combinatorics, Poisson distribution, Compound Poisson process
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