AGGREGATION OF INDEPENDENT PARETIAN RANDOM VARIAB LES
BERTRAND ROEHNER,* Laboratoire de Physique Théorique et Hautes Energies,t Paris
PETER WINIWARTER$++
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.