Pareto Distribution, Fat Tails, Power Law Distribution, Zipf Law

C1, C6, C8

This short note analyzes the distributional properties of Pareto Type III random variables. We introduce a three parameters version of the orignal two parameters distribution proposed by Pareto and derive both the density and the characteristic function. The analytic expression of the inverse distribution function is also obtained, together with a simple series expansion of its moments of any order. Finally, we propose a simple statistical exercise designed to show the increased reliability of the Pareto Type III distribution in describing asymptotically dumped power-like behaviors.