Cauchy Distribution

Cauchy distribution, also known as Cauchy-Lorentz distribution, in statistics, continuous distribution function with two parameters, first studied early in the 19th century by French mathematician Augustin-Louis Cauchy. It was later applied by the 19th-century Dutch physicist Hendrik Lorentz to explain forced resonance, or vibrations. At a glance, the Cauchy distribution may look like the normal distribution, but its “tails” do not taper off nearly as quickly as those of the normal distribution.

With location parameter t (the median for the distribution, it does not have a mean) and scale parameter s, the probability density function for the Cauchy distribution is The case in which s = 1 and t = 0 is known as the standard Cauchy distribution, which is given by