On the Poisson-binomial relative error

This paper analyses the goodness of Poisson approximation to the binomial distribution with parameters n and p. In order to stress the importance of the smallness of p to obtain a good approximation, the relative error is analysed when p is fixed and n tends to infinity. We find the relative error pointwise limit and its asymptotic distribution; we also show that the asymptotic mean relative error gives an approximation of the mean relative error. Finally we give numerical estimates of all these approximations.