Cauchy cdf
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Revision as of 15:41, 9 March 2018 by Tom (talk | contribs) (Created page with "The Cauchy cumulative distribution function $F \colon \mathbb{R} \rightarrow \mathbb{R}$ for $x_0 \in \mathbb{R}$ and $\gamma > 0$ is given by $$F(x) = \dfrac{1}{\pi} \mat...")
The Cauchy cumulative distribution function $F \colon \mathbb{R} \rightarrow \mathbb{R}$ for $x_0 \in \mathbb{R}$ and $\gamma > 0$ is given by $$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.
