Reexamining Key Applications of the Poisson Distribution

The Poisson distribution is a discrete probability model, widely used in science and engineering to describe various natural and man-made phenomena. It possesses an important feature, namely being inherently asymmetric, but as its parameter becomes large, the distribution becomes approximately symmetric. To broaden its use, multiple extensions and variations have been developed. Determining whether a data set follows a Poisson distribution involves hypothesis testing at a chosen significance level. When sampling from a Poisson distribution, confidence intervals provide an estimated range instead of a single value. Due to the discrete nature of the Poisson distribution, confidence intervals cannot be derived from a simple formula, and are therefore computed using specialized algorithms. In this paper, three alternatives are given and discussed.