Editing Cauchy distribution (section)

===General===
*<math>\operatorname{Cauchy}(0,1) \sim \textrm{t}(\mathrm{df}=1)\,</math> [[Student's t distribution|Student's ''t'' distribution]]
*<math>\operatorname{Cauchy}(\mu,\sigma) \sim \textrm{t}_{(\mathrm{df}=1)}(\mu,\sigma)\,</math> [[Student's t distribution#location-scale|non-standardized Student's ''t'' distribution]]
*If <math>X, Y \sim \textrm{N}(0,1)\, X, Y</math> independent, then <math> \tfrac X Y\sim \textrm{Cauchy}(0,1)\,</math>
*If <math>X \sim \textrm{U}(0,1)\,</math> then <math> \tan \left( \pi \left(X-\tfrac{1}{2}\right) \right) \sim \textrm{Cauchy}(0,1)\,</math>
*If <math>X \sim \operatorname{Log-Cauchy}(0, 1)</math> then <math>\ln(X) \sim \textrm{Cauchy}(0, 1)</math>
*If <math>X \sim \operatorname{Cauchy}(x_0,\gamma)</math>  then <math>\tfrac1X \sim \operatorname{Cauchy}\left(\tfrac{x_0}{x_0^2+\gamma^2},\tfrac{\gamma}{x_0^2+\gamma^2}\right)</math> 
*The Cauchy distribution is a limiting case of a [[Pearson distribution]] of type 4{{Citation needed|date=March 2011}}
*The Cauchy distribution is a special case of a [[Pearson distribution]] of type 7.<ref name=jkb1/>
*The Cauchy distribution is a [[stable distribution]]: if <math>X \sim \textrm{Stable}(1, 0, \gamma, \mu)</math>, then <math>X \sim \operatorname{Cauchy}(\mu, \gamma)</math>.
*The Cauchy distribution is a singular limit of a [[hyperbolic distribution]]{{Citation needed|date=April 2011}}
*The [[wrapped Cauchy distribution]], taking values on a circle, is derived from the Cauchy distribution by wrapping it around the circle.
*If <math>X \sim \textrm{N}(0,1)</math>, <math>Z \sim \operatorname{Inverse-Gamma}(1/2, s^2/2)</math>, then <math>Y = \mu + X \sqrt Z \sim \operatorname{Cauchy}(\mu,s)</math>. For half-Cauchy distributions, the relation holds by setting <math>X \sim \textrm{N}(0,1) I\{X\ge0\}</math>.