## Cauchy-Lorentz Distribution

.. ratio of two independent normally distributed random variables with mean zero.

Lorentz distribution is frequently used in physics.

PDF:

$$\frac{1}{\pi\gamma} \left( \frac{\gamma^2}{ (x-x_0)^2 + \gamma^2} \right)$$

The median and mode of the Cauchy-Lorentz distribution is always $x_0$. $\gamma$ is the FWHM.

## Visualize

Published: by ;

Lei Ma (2020). 'Cauchy-Lorentz Distribution', Datumorphism, 03 April. Available at: https://datumorphism.leima.is/cards/statistics/distributions/cauchy/.