The Cauchy cumulative distribution function is defined for all real numbers α, and for positive β, by the integral
The following plots show probability density functions
CauchyDen(x;α, β) and cumulative distribution functions
CauchyDist(x;α, β), for the parameters
α, β
= (- 3, 1), (0, 1.5), and (3, 1), and
-5≤x≤5.