Strategies for efficient computation of multivariate poisson probabilities

The main reason for the limited use of multivariate discrete models is the difficulty in calculating the required probabilities. The task is usually undertaken via recursive relationships which become quite computationally demanding for high dimensions and large values. The present paper discusses efficient algorithms that make use of the recurrence relationships in a manner that reduces the computational effort and thus allow for easy and cheap calculation of the probabilities. The most common multivariate discrete distribution, the multivariate Poisson distribution is treated. Real data problems are provided to motivate the use of the proposed strategies. Extensions of our results are discussed. It is shown that probabilities, for a large family of multivariate distributions, can be computed efficiently via our algorithms.