Cauchy-Lorentz Distribution

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#Statistics #Distributions

Cauchy-Lorentz Distribution

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

Source: https://en.wikipedia.org/wiki/Cauchy_distribution

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

Planted: by ;

References:
  1. Cauchy Distribution @ Wikipedia
  2. stdlib.js documentation
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L Ma (2020). 'Cauchy-Lorentz Distribution', Datumorphism, 03 April. Available at: https://datumorphism.leima.is/cards/statistics/distributions/cauchy/.