# Category:Cauchy Distribution

Jump to navigation
Jump to search

This category contains results about the Cauchy distribution.

Let $X$ be a continuous random variable on a probability space $\struct {\Omega, \Sigma, \Pr}$.

Let $\Img X = \R$.

$X$ is said to have a **Cauchy distribution** if it has probability density function:

- $\map {f_X} x = \dfrac 1 {\pi \gamma \paren {1 + \paren {\frac {x - x_0} \gamma}^2} }$

for some $\gamma > 0$.

This is written:

- $X \sim \Cauchy {x_0} \gamma$

*This category currently contains no pages or media.*