On the computation of poisson probabilities

The Poisson distribution is a distribution commonly used in statistics. It also plays a central role in the analysis of the transient behaviour of continuous-time Markov chains. Several methods have been devised for evaluating using floating-point arithmetic the probability mass function (PMF) of the Poisson distribution. Restricting our attention to published methods intended for the computation of a single probability or a few of them, we show that neither of them is completely satisfactory in terms of accuracy. With that motivation, we develop a new method for the evaluation of the PDF of the Poisson distribution. The method is intended for the computation of a single probability or a few of them. Numerical experimentation illustrates that the method can be more accurate and slightly faster than the previous methods. Besides, the method comes with guaranteed approximation relative error.Postprint (author's final draft