Cauchy–Lorentz standar distribution (cumulative distribution function)

Description

In probability and statistics,the Cauchy distribution, is a continuous probability distribution. The simplest Cauchy distribution is called the standard Cauchy distribution. It is the distribution of a random variable that is the ratio of two independent standard normal variables. When U and V are two independent normally distributed random variables with expected value 0 and variance 1, then the ratio U/V has the standard Cauchy distribution.
Its cumulative distribution function F(x; 0,1) has the shape of an arctangent function.

Related formulas

Variables

FCumulative distribution function (dimensionless)
πpi
xVariable (dimensionless)
γ The scale parameter ( γ = 1 ) (dimensionless)