Cauchy distribution
The log-Cauchy distribution is an example of a heavy-tailed distribution. Some authors regard it as a "super-heavy tailed" distribution, because it has a heavier tail than a Pareto distribution-type heavy tail, i.e., it has a logarithmically decaying tail. As with the Cauchy distribution, none of the non-trivial moments of the log-Cauchy distribution are finite. The mean is a moment so the log-Cauchy distribution does not have a defined mean or standard deviation.