Siméon-Denis Poisson (1781-1840)

Siméon-Denis Poisson was educated as a child by his family and then at secondary school. He went on to study at École Polytechnique. While there, he was mentored and supported by Pierre Simon de Laplace (1749-1827) who helped him get a job as a professor at École Polytechnique. He later became the first Professor of Mechanics at the University of Paris. When Napoleon fell from power in 1815, Poisson was appointed to a position over scientific education in all of France.

Poisson is most remembered for the distribution named after him, the Poisson distribution. He wrote about this distribution in Recherches sur la probabilitédes jugements en matière criminelle et en matière civile, framing it in the context of the relationship between the likelihood of convicting someone put on trial and the likelihood that the individual actually committed the crime. This would allow estimation of the number of innocent people in jail, but would not identify which were innocent. Other applications of this distribution were limited for many years.

Though his name is most recognizable because of the distribution, he would have considered it one of his minor contributions to statistics, in part because Abraham de Moivre (1667-1754) had already written about it. Poisson published the Law of Large Numbers in 1835, which said that the proportion of successes in independent trials will follow a pattern in the long run even if there is great unpredictability in the short run. It was a generalization of Bernoulli's law. He was the first to prove Laplace's Theorem which indicates that the sum of many errors from any given distribution will asymptotically approach a Gaussian distribution. He was also one of the first to look at a theory for errors that didn't follow a Gaussian distribution.

Poisson's contributions were not limited to probability. He worked with differential equations of mechanics, definite integrals, Poisson brackets in analysis, and Poisson's integral.