Despite its name, the Poisson point process was neither discovered nor studied by theits Frenchnamesake. mathematician [[Siméon Denis Poisson]]; the nameIt is cited as an example of [[Stigler's law of eponymy]].<ref name="Stirzaker2000"/><ref name="GuttorpThorarinsdottir2012"/> The name stemsarises from itsthe process's inherent relation to the [[Poisson distribution]], derived by Poisson as a limiting case of the [[binomial distribution]].<ref name="Good1986">{{cite journal|last1=Good|first1=I. J.|title=Some Statistical Applications of Poisson's Work|journal=Statistical Science|volume=1|issue=2|year=1986|pages=157–170|issn=0883-4237|doi=10.1214/ss/1177013690|doi-access=free}}</ref> ThisIt describes the [[probability]] of the sum of <math>\textstyle n</math> [[Bernoulli trialstrial]]s with probability <math>\textstyle p</math>, often likened to the number of heads (or tails) after <math>\textstyle n</math> biased [[Coin flipping|coin flips]] of a coin with the probability of a head (or tail) occurring being <math>\textstyle p</math>. For some positive constant <math>\textstyle \Lambda>0</math>, as <math>\textstyle n</math> increases towards infinity and <math>\textstyle p</math> decreases towards zero such that the product <math>\textstyle np=\Lambda</math> is fixed, the Poisson distribution more closely approximates that of the binomial.<ref name="grimmett2001probability">{{cite book |first1=G. |last1=Grimmett |first2=D. |last2=Stirzaker |title=Probability and Random Processes |publisher=Oxford University Press |edition=3rd |year=2001 |isbn=0-19-857222-0 }}</ref>
Poisson derived the Poisson distribution, published in 1841, by examining the binomial distribution in the [[Limit (mathematics)|limit]] of <math>\textstyle p</math> (to zero) and <math>\textstyle n</math> (to infinity). It only appears once in all of Poisson's work,<ref name="stigler1982poisson">{{cite journal |first=S. M. |last=Stigler |title=Poisson on the Poisson Distribution |journal=Statistics & Probability Letters |volume=1 |issue=1 |pages=33–35 |year=1982 |doi=10.1016/0167-7152(82)90010-4 }}</ref> and the result was not well known during his time. Over the following years a number of peopleothers used the distribution without citing Poisson, including [[Philipp Ludwig von Seidel]] and [[Ernst Abbe]].{{sfnp|Daley|Vere-Jones|2003|pages=8–9}}
<ref name="Stirzaker2000" /> At the end of the 19th century, [[Ladislaus Bortkiewicz]] would studystudied the distribution, again in a different setting (citing Poisson), using the distribution with real data to studyon the number of deaths from horse kicks in the [[Prussian army]].<ref name="Good1986" /><ref name="quine1987bortkiewicz">{{cite journal |first1=M. |last1=Quine |first2=E. |last2=Seneta |title=Bortkiewicz's data and the law of small numbers |journal=International Statistical Review |volume=55 |issue=2 |pages=173–181 |year=1987 |doi=10.2307/1403193 |jstor=1403193 }}</ref>
