If location
or scale
are not specified, they assume
the default values of 0
and 1
respectively. The Cauchy distribution with location $l$ and scale $s$ has
density
$$f(x) = \frac{1}{\pi s}
\left( 1 + \left(\frac{x - l}{s}\right)^2 \right)^{-1}$$
for all $x$.
The generation algorithm uses fast numerical inversion. The parameters
lb
and ub
can be used to generate variates from
the Cauchy distribution truncated to the interval (lb
,ub
).