Definition:Cauchy Distribution/Scale Parameter

Definition

Let $X$ be a continuous random variable with a Cauchy distribution:

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

for:

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

$\gamma \in \R$

The parameter $\lambda$ is referred to as the scale parameter of $X$.

Also see

• Results about the Cauchy distribution can be found here.

Sources

• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Cauchy distribution