The formula for this curve is so much easier to deal with versus the normal distribution. Perhaps it should be used more. You can see above that it is pretty much inadequate since its theoretical statistics are not well-defined. In the interactive cell below, you might notice some issues right away by comparing the Cauchy probabilty function against a normal probability function (when \(\mu = 0\) but with varied standard deviations. Notice especially that as you change the normal distribution’s \(\sigma_{\text{normal}}\) the the area you see under the normal curve totally overwhelms the area in the stationary Cauchy distribution. That means that the two tails of the Cauchy distribution have a lot more area far away from zero than the nomal distribution. This is one of the issues why the Cauchy doesn’t give good results.