Exactly Computing the Tail of the Poisson-Binomial Distribution

We present ShiftConvolvePoibin, a fast exact method to compute the tail of a Poisson-binomial distribution (PBD). Our method employs an exponential shift to retain its accuracy when computing a tail probability, and in practice we find that it is immune to the significant relative errors that other methods, exact or approximate, can suffer from when computing very small tail probabilities of the PBD. The accompanying R package is also competitive with the fastest implementations for computing the entire PBD.