Category:Definitions/Cauchy Distribution

This category contains definitions related to Cauchy Distribution.
Related results can be found in Category: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:

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

for:

$\lambda \in \R_{>0}$

$\gamma \in \R$

This is written:

$X \sim \Cauchy \gamma \lambda$