Efficient computation for the Poisson binomial distribution

Direct construction of the probability distribution function for a Poisson binomial random variable, where success probabilities may vary from trial to trial, requires on the order of 2 n calculations, and is computationally infeasible for all but modest sized problems. An approach offered by Thomas and Taub (J Stat Comput Simul 14:125–131 1982 ) reduces this effort to approximately n 2 , which, while certainly an improvement, can still be significant for large values of n . We offer modifications to the method of Thomas and Taub that greatly reduce the computations while still delivering highly accurate results.