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.

Related formulas

Variables

fxProbability density function (dimensionless)
πpi
γThe scale parameter (equal to half the interquartile range) (dimensionless)
xVariable (dimensionless)
x0The location parameter, specifying the location of the peak of the distribution (dimensionless)