Poisson Random Variate Generation

SUMMARY The paper examines the problem of generating Poisson random variates particularly when the parameter x may vary from call to call. A new algorithm based on a unidirectional search from the mode is proposed; the modal probability and modal cumulative probability, when required, are calculated by simple and rapid, yet extremely accurate, asymptotic approximations; a squeeze feature is incorporated. Timings for a Fortran 77 implementation show that the algorithm dominates the current state‐of‐the‐art algorithms for λ<700.