[DaniFong]

The calculated standard deviation from any finite sample size of a long tailed distribution (e.g. Pareto with alpha <= 2) will be off by a factor of infinity.The point is that, not only is the standard deviation irrecoverable in this case, but it's hardly the figure of merit if you do know it.

[gambling8nt]

Except that in real life there are no distributions with support outside of a finite interval in space or time; there's always some point when you stop running the system...if some packets don't arrive by that point, you generally don't care how much longer they would have taken.