A Poisson-binomial relative error uniform bound

In this paper, we use the Stein–Chen method and the characterization associated with the binomial random variable to determine a uniform bound on the relative error of binomial and Poisson cumulative distribution functions. In addition, we also give uniform lower and upper bounds of the ratio of two such cumulative distribution functions. For these bounds, it is indicated that each result gives a good Poisson approximation if pp or λλ is small and nn is large, where nn and pp are parameters of the binomial distribution and λ=npλ=np is the parameter of the Poisson distribution.