# Cauchy cdf

The Cauchy cumulative distribution function $F \colon \mathbb{R} \rightarrow \mathbb{R}$ for $x_0 \in \mathbb{R}$ and $\gamma > 0$ is given by $$F(x) = \dfrac{1}{\pi} \mathrm{arctan} \left( \dfrac{x-x_0}{\gamma} \right) + \dfrac{1}{2},$$ where $\pi$ denotes pi and $\arctan$ denotes arctan.