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.

摘要

尽管它是一种广泛使用且被误用的离散分布，但教科书倾向于对泊松分布的历史视而不见，通常将其抽象地推导出为二项式的极限情况。很少提及那些利用空间和时间考虑独立推导出它并在工作中使用它的生物和物理科学家。将其应用于涉及人类活动/行为的计数也不困难。我们 (a) 勾勒泊松分布的早期历史 (b) 使用原始的生物和物理应用，以及它们的现代多媒体重演，说明涉及空间和时间的泊松分布原理，以及 (c) 激发计数分布会计对于额外的泊松变化。回放的历史应用可以帮助今天的学生，