The Cauchy-Lorentz distribution, named after Augustin Cauchy and Hendrik Lorentz, is a continuous probability distribution. As a probability distribution, it is known as the Cauchy distribution while among physicists it is known as a Lorentz distribution, a Lorentz(ian) function or the Breit-Wigner distribution. Its importance in physics is due to it being the solution to the differential equation describing forced resonance. In spectroscopy it is the description of the line shape of spectral lines which are broadened by many mechanisms, in particular, collision broadening.

The probability density function of the Cauchy-Lorentz distribution is:

f(x,t,s) = 1/pis/(s^2(x-t)^2)

support -inf ⇐ x ⇐ inf