Cauchy Distribution

A probability distribution \(Cauchy(\mu, \sigma)\) having the PDF
\[ p_{\mu, \sigma}(x) = \left(\pi\sigma \left(1 + \left(\frac{x-\mu}{\sigma}\right)^2\right)\right)^{-1} \]
If \(\mu\) is equal to zero and \(\sigma\) is equal to one then it is known as the standard Cauchy distribution and governs the ratio of independent standard normal random variables.