On the Computation of Poisson Probabilities

S. D. Chagaboina, J. A. Carrasco López, V. Suñé Socias

he 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.

Keywords: Poisson distribution Poisson probabilities numerical methods

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