where x_0 is the location parameter, specifying the location of the peak of the distribution, and \gamma is the scale parameter which specifies the half-width at half-maximum (HWHM), alternatively 2\gamma is full width at half maximum (FWHM). \gamma is also equal to half the interquartile range and is sometimes called the probable error. Augustin-Louis Cauchy exploited such a density function in 1827 with an infinitesimal scale parameter, defining what would now be called a Dirac delta function.
