Aggregation of independent Paretian random variables

Abstract

Empirical Paretian distributions play an important role in urban demography, size distributions of firms and income distributions; hence the addition of Paretian random variables is of interest. First, we give the asymptotic behavior (for large values of the variable) of the density function of a sum of n independently distributed Paretian variables. We then obtain the limiting distribution of an infinite sum of (i.i.d) Paretian variables and link our results with the theory of stable distributions.