HyperQuick algorithm for discrete hypergeometric distribution

Based on the binomial identity∑k=0x(Mk)(N−Mn−k)=∑m=MN−n+x(mx)(N−1−mN−m−n+x) we present an algorithm for computing the cumulative distribution function of a random variable with discrete hypergeometric distribution. For any accuracy ϵ⩾0ϵ⩾0 the required number of computational cycles is less then N−nN−n, where N is the size of the population and n is the size of the sample. In this article we prove the binomial identity above and give the formula for the number of computational cycles required to achieve the desired accuracy for an arbitrary set of parameters.