The Cauchy-Lorentz distribution. It's also known as Lorentz distribution or Breit–Wigner distribution.
It doesn't have mean and variance.
Central value of Cauchy-Lorentz distribution which is its mode and median. Distribution doesn't have mean so function is named after median.
Scale parameter of Cauchy-Lorentz distribution. It's different from variance and specify half width at half maximum (HWHM).