2.1.1.10. Cauchy law

This law describes a Cauchy-Lorentz distribution with a location parameter \(x_0\) and a scale parameter \(\gamma\), as

\[f(x) = \frac{\gamma}{\pi\times(\gamma^{2}+(x-x_{0})^{2})}\]

The mean and standard deviation of this distribution are not properly defined.

Figure 2.11 shows the PDF, CDF and inverse CDF generated for different sets of parameters.

../../../_images/TCauchyDistribution.png

Figure 2.11 Example of PDF, CDF and inverse CDF for Cauchy distributions.