Cauchy-Lorentz Distribution

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.

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

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

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Current Ref:

  • cards/statistics/distributions/cauchy.md