Definition:Cauchy Distribution/Also presented as

Cauchy Distribution: Also presented as
Let $X$ be a continuous random variable on a probability space $\struct {\Omega, \Sigma, \Pr}$.

Let $\Img X = \R$. The Cauchy Distribution of $X$ can be found expressed in the form:


 * $\map {f_X} x = \dfrac \lambda {\pi \paren {\lambda^2 + \paren {x - \gamma}^2} }$

for:
 * $\lambda \in \R_{>0}$
 * $\gamma \in \R$

This is written:


 * $X \sim \Cauchy \gamma \lambda$