Poisson Distribution for various values of λ |

*Research on the Probability of Criminal and Civil Verdicts.*

^{1}It was published in 1837, just three years before Poisson's death, and did not have a great impact at the time.

His distribution was brought to greater prominence by Ladislaus Josephovich Bortkiewicz (1868-1931), a Polish statistician. In 1898 he published a book entitled, in English translation,

*The Law of Small Numbers*, in which he showed that the Poisson distribution held for events even when the probabilities varied. His examples were the number of men killed by horse kicks in the Prussian army over a 20 year period and the number of children who committed suicide in Prussia. His work brought the Poisson distribution to a wider audience, and it is often called the Law of Small Numbers today. As you can see, the Poisson distribution can be applied to many different situations, and some modern applications include the number of calls that a cell tower receives and the number of beds that an emergency room needs to have available.

[1] For a more detailed discussion of Poisson's work, see "A Study of Poisson's Models for Jury Verdicts in Criminal and Civil Trials" by Alan E. Gelfand and Herbert Solomon in the

*Journal of the American Statistical Association*, Vol. 68, No. 342 (Jun., 1973), pp. 271-278.

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