Poisson point process
Poisson distribution

Despite its name, the Poisson point process was neither discovered nor studied by its namesake. It is cited as an example of Stigler's law of eponymy. The name arises from the process's inherent relation to the Poisson distribution, derived by Poisson as a limiting case of the binomial distribution. It describes the probability of the sum of n {\displaystyle \textstyle n} Bernoulli trials with probability p {\displaystyle \textstyle p}, often likened to the number of heads (or tails) after n {\displaystyle \textstyle n} biased coin flips with the probability of a head (or tail) occurring being p {\displaystyle \textstyle p}. For some positive constant Λ > 0 {\displaystyle \textstyle \Lambda >0}, as n {\displaystyle \textstyle n} increases towards infinity and p {\displaystyle \textstyle p} decreases towards zero such that the product n p = Λ {\displaystyle \textstyle np=\Lambda } is fixed, the Poisson distribution more closely approximates that of the binomial.

Poisson derived the Poisson distribution, published in 1841, by examining the binomial distribution in the limit of p {\displaystyle \textstyle p} (to zero) and n {\displaystyle \textstyle n} (to infinity). It only appears once in all of Poisson's work, and the result was not well known during his time. Over the following years others used the distribution without citing Poisson, including Philipp Ludwig von Seidel and Ernst Abbe. At the end of the 19th century, Ladislaus Bortkiewicz studied the distribution, citing Poisson, using real data on the number of deaths from horse kicks in the Prussian army.
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