Cauchy distribution

What is Cauchy Distribution?

Cauchy distribution is the distribution of a uniformly distributed angle ray’s x-intercept in a continuous probability distribution. In machine learning, this is used as an alternative to either the Normal or Levy distribution formulas to describe resonance behavior.

Also called the Lorentz distribution, this stable distribution is defined as:

f(x; x0,γ)

What is Cauchy Distribution used for?

Unlike probability models under the Central Limit Theorem, this distribution has no finite moments of order greater than or equal to one and it has no moment generating function. This makes the Cauchy formula quite useful for analytical modeling of any field dealing with infinite exponential growth.

Adding to its flexibility, this distribution only has the mode and median defined, as x0, with no mean, variance or higher moments defined. 

Cauchy Distribution is also the most common probability density alternative to using Normal or Gaussian Distribution for Estimation of Distribution Algorithms (EDA).