The “Poisson” Distribution: History, Reenactments, Adaptations

Abstract

Although it is a widely used—and misused—discrete distribution, textbooks tend to give the history of the Poisson distribution short shrift, typically deriving it in the abstract as a limiting case of a binomial. The biological and physical scientists who independently derived it using space and time considerations and used it in their work are seldom mentioned. Nor are the difficulties of applying it to counts involving human activities/behavior. We (a) sketch the early history of the Poisson distribution (b) illustrate principles of the Poisson distribution involving space and time using the original biological and physical applications, as well as modern multimedia reenactments of them, and (c) motivate count distributions accounting for extra-Poisson variation. The replayed historical applications can help today’s students, teachers and practitioners to see or hear what randomness looks or sounds like, to get practice in the practicalities of “counting statistics,” to distinguish situations where the pure Poisson distribution does and doesn’t hold—and to think about what one might do when it doesn’t.