2007/07 LEM Working Paper Series


On the Pareto Type III Distribution

Giulio Bottazzi
  Keywords
 
Pareto Distribution, Fat Tails, Power Law Distribution, Zipf Law


  JEL Classifications
 
C1, C6, C8


  Abstract
 
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.


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