Its mode and median are zero, but the expectation value, variance and higher moments are undefined since the corresponding integrals diverge. A commonly used measure of the width is the full width at half maximum (FWHM), which is equal to 2.
If a variable 
is uniformly distributed between 
and 
, then 
will follow a Cauchy distribution. If y and z follow independent normal distributions, x=y/z will again follow a Cauchy distribution.
A more general form of the Cauchy distribution is the Lorentz distribution , also called the Breit-Wigner distribution which has the probability density
where x0 is the mode and 
the full width at half maximum or FWHM.