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We use the Stein-Chen method to determine a bound on the rel- ative error between the Poisson binomial distribution function with parameter p = (p1,...,pn) and the Poisson distribution function with mean  = P n=1 pi 1 pi . With this bound, the Poisson distribution function with this mean can be used as an estimate of the Poisson binomial distribution function whenever all pi are small.

A BOUND ON THE POISSON BINOMIAL-POISSON RELATIVE ERROR