Cauchy distribution

Named after Augustin Cauchy.

Cauchy distribution (plural Cauchy distributions)

1. (statistics) A symmetric continuous probability distribution with fat tails, with probability density function that is

   ${\displaystyle {\begin{aligned}f(x;x_{0},\gamma )&={\frac {1}{\pi \gamma \left[1+\left({\frac {x-x_{0}}{\gamma }}\right)^{2}\right]}}&={1 \over \pi }\left[{\gamma \over (x-x_{0})^{2}+\gamma ^{2}}\right]\end{aligned}}}$

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