Log Cauchy distribution as lifetime distribution Though I know that the moments of Log-Cauchy distribution do not exist, is it possible to use the Log-Cauchy distribution as a lifetime distribution under Type-II censoring?  Because the MLE of the parameters under censoring can be calculated using numerical methods.
I just want to know if having no moments makes Log-Cauchy distribution a poor choice to be used as a Lifetime distribution under censored data. Because it is a Super heavy tailed distribution, and in certain situations, might provide a better fit.

There's no mathematical problem with using a log-Cauchy distribution, but it's going to be hard to say anything about it being a better fit when the very long tail is heavily censored.
