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Aggregation of independent Paretian random variables

Published online by Cambridge University Press:  01 July 2016

Bertrand Roehner  and
Peter Winiwarter
Bertrand Roehner*
Affiliation:
Laboratoire de Physique Théorique et Hautes Energies,† Paris
Peter Winiwarter*
Affiliation:
Laboratoire de Physique Théorique et Hautes Energies,† Paris
*
∗Postal address: Université Paris VII, Tour 14-24, 5ème étage, 2, place Jussieu, 75251 Paris Cedex 05, France.
‡Postal address: Le Bordalier, F41270 Droné, France.
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Abstract

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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.

Type
Letters to the Editor
Information
Advances in Applied Probability , Volume 17 , Issue 2 , June 1985 , pp. 465 - 469
Copyright
Copyright © Applied Probability Trust 1985 

Footnotes

†

Laboratoire associé au CNRS LA 280.

References

Doetsch, G. (1950) Handbuch der Laplace-Transformation , Vol. 1. Birkhaüser, Basel.Google Scholar
Gnedenko, B. V. and Kolmogorov, A. N. (1954) Limit Distributions for Sums of Independent Random Variables. Addison-Wesley, Reading, Mass.Google Scholar
Hart, P. E. and Prais, S. J. (1956) The analysis of business concentration: a statistical approach. J. R. Statist. Soc. , A119, 150–191.Google Scholar
Lösch, F. and Schoblick, F. (1951) Die Fakultät (Gamma Funktion) und verwandte Funktionen. Teubner, Leipzig.Google Scholar
Magnus, W., Oberhettinger, F. and Soni, R. P. (1966) Formulas and Theorems for the Special Functions of Mathematical Physics. Springer-Verlag, New York.Google Scholar
Mandelbrot, B. (1960) The Pareto-Lévy law and the distribution of income. Internat. Econom. Rev. 1, 79–106.Google Scholar
Press, S. J. (1982) Applied Multivariate Analysis. R. E. Krieger, Malabar, Rorida.Google Scholar
Pumain, D. (1982) La dynamique des villes. Economica, Paris.Google Scholar
Quandt, R. E. (1964) Statistical discrimination among alternative hypothesis and some economic regularities. J. Regional Sci. 5(2), 1–23.Google Scholar
Roehner, B. and Wiese, K. E. (1982) A dynamic generalization of Zipf’s rank-size rule. Environment and Planning A 14, 1449–1467.Google Scholar
Simon, H. A. and Bonini, C. P. (1958) The size distribution of business firms. American Econom. Rev. 48, 607–617.Google Scholar
Steindl, J. (1965) Random Processes and the Growth of Firms. Hafner, New York Google Scholar
Zipf, G. K. (1948) Human Behavior and the Principle of Least Effort. Addison-Wesley, Cambridge, Mass.Google Scholar