Cauchy

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The Cauchy distribution is a continuous probability distribution named after the French mathematician Augustin Cauchy. It is also known as the Lorentzian distribution. It is characterized by its "thick-tailed" shape, meaning that it has a more significant proportion of data points in the tails of the distribution than other common distributions like the normal distribution.

The Cauchy distribution has a PDF (probability density function) given by:

f(x) = \frac{1}{\pi}\cdot \frac{d}{d^2 + (x - m)^2} = \frac{1}{\pi d (1 + (\frac{x-m}{d})^2)}