Cauchy distribution

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The Cauchy-Lorentz distribution (after Augustin-Louis Cauchy and Hendrik Lorentz) is a continuous probability distribution. As a probability distribution it is usually called a Cauchy distribution. Physicists know it as a Lorentz distribution.

It is used in spectroscopy to describe the spectral lines found there, and to describe resonance.[1]

The Cauchy distribution is often used in statistics as the canonical example of a "pathological" distribution. Both its mean and its variance are undefined.

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