On the Pareto Type III Distribution

Abstract

This note analyzes some properties of the Pareto Type III distribution. A three parameter version of the original two parameter distribution proposed by Pareto is introduced and both its density and characteristic function are derived. The analytic expression of the inverse distribution function is also obtained, together with an explicit expression of its moments of any order. Finally, a simple statistical exercise is proposed, designed to show the reliability of the Pareto Type III distribution in describing asymptotically dumped power-like behaviors.