Cauchy–Lorentz distribution (probability density function)
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.
|fx||Probability density function (dimensionless)|
|γ||The scale parameter (equal to half the interquartile range) (dimensionless)|
|x0||The location parameter, specifying the location of the peak of the distribution (dimensionless)|