# Cauchy–Lorentz distribution (cumulative distribution function)

## Description

In probability and statistics,the Cauchy distribution, is a continuous probability distribution. The Cauchy distribution is often used in statistics as the canonical example of a “pathological” distribution since both its mean and its variance are undefined. The Cauchy distribution does not have finite moments of order greater than or equal to one; only fractional absolute moments exist.The Cauchy distribution has no moment generating function.

Its cumulative distribution function has the shape of an arctangent function( thinking the variables as angles in radians).

## Variables

F_{x} | Cumulative distribution function (in a shape of arctanx function) (radians) |

π | pi |

x | Variable (radians) |

x_{0} | The location parameter, specifying the location of the peak of the distribution (radians) |

γ | The scale parameter (equal to half the interquartile range) (dimensionless) |