The Cauchy distribution (the term first used by Uspensky, 1937) has density function:

f(x) = 1/(qp*{1+[(x-h)/q]2})

0 < q

where

h |
is the location parameter (median) |

q |
is the scale parameter |

p |
is the constant Pi (3.14...) |

The animation above shows the shape of the Cauchy distribution when the location parameter equals 0 and the scale parameter equals 1. Note that C represents the critical value from the Cauchy distribution displayed in the animation. For a complete listing of all distribution functions, see Distributions and Their Functions.