Simple and Efficient Algorithms for Computing Exact Cumulative Discrete Probabilities and its Inverses

摘要

This paper deals with the computation of exact cumulative probabilities of discrete distributions and its inverses. For the computation of cumulative probabilities an efficient and universal algorithm of 15 lines is presented, which can be applied to the most important discrete distributions (e.g. the binomial, the poisson and the hypergeometric distribution). With a slight modification an algorithm of 20 lines is obtained for the calculation of the respective inverse distributions. The accuracy of both algorithms can be specified. Both algorithms are simple, very fast and numerically stable even if the sample size is one billion.