# Cauchy–Lorentz distribution (probability density function)

## Description

In probability and statistics,the Cauchy distribution, is a continuous probability distribution. The probability density function (pdf), or density of a continuous random variable, is a function that describes the relative likelihood for this random variable to take on a given value.

The location parameter, species the location of the peak of the distribution, and γ is the scale parameter which specifies the half-width at half-maximum (HWHM), alternatively 2γ is full width at half maximum (FWHM). γ is also equal to half the interquartile range and is sometimes called the probable error.

## Variables

f_{x} | Probability density function (dimensionless) |

π | pi |

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

x | Variable (dimensionless) |

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