Editing Cauchy distribution (section)

==History==
[[File:Mean estimator consistency.gif|thumb|upright=1.35|right|Estimating the mean and standard deviation through a sample from a Cauchy distribution (bottom) does not converge as the size of the sample grows, as in the [[normal distribution]] (top). There can be arbitrarily large jumps in the estimates, as seen in the graphs on the bottom. (Click to expand)]]
A function with the form of the density function of the Cauchy distribution was studied geometrically by [[Pierre de Fermat|Fermat]] in 1659, and later was known as the [[witch of Agnesi]], after [[Maria Gaetana Agnesi]] included it as an example in her 1748 calculus textbook. Despite its name, the first explicit analysis of the properties of the Cauchy distribution was published by the French mathematician [[Siméon Denis Poisson|Poisson]] in 1824, with Cauchy only becoming associated with it during an academic controversy in 1853.<ref>Cauchy and the Witch of Agnesi in ''Statistics on the Table'', S M Stigler Harvard 1999 Chapter 18</ref> Poisson noted that if the mean of observations following such a distribution were taken, the [[standard deviation]] did not converge to any finite number. As such, [[Pierre-Simon Laplace|Laplace]]'s use of the [[central limit theorem]] with such a distribution was inappropriate, as it assumed a finite mean and variance. Despite this, Poisson did not regard the issue as important, in contrast to [[Irénée-Jules Bienaymé|Bienaymé]], who was to engage Cauchy in a long dispute over the matter.