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May, 1974 A Characterization of the Pareto Distribution
Nagesh S. Revankar, Michael J. Hartley, Marcello Pagano
Ann. Statist. 2(3): 599-601 (May, 1974). DOI: 10.1214/aos/1176342723


A positive random variable $X$ whose mean exists, has a Pareto distribution if, and only if, $E(X \mid X > x) = h + gx$ for $g > 1$. This characterization was motivated by the fact that the Pareto distribution has been widely used to model income. Now, suppose that individuals under-report their income for income tax purposes. If one assumes that for a given income, the average under-reporting is a constant fraction of the amount by which the income exceeds the tax exempt level, then the average under-reporting error for a given reported income is a linear function of the reported income if, and only if, incomes follow a Pareto distribution.


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Nagesh S. Revankar. Michael J. Hartley. Marcello Pagano. "A Characterization of the Pareto Distribution." Ann. Statist. 2 (3) 599 - 601, May, 1974.


Published: May, 1974
First available in Project Euclid: 12 April 2007

zbMATH: 0282.60010
MathSciNet: MR353534
Digital Object Identifier: 10.1214/aos/1176342723

Primary: 62E10
Secondary: 62P20

Keywords: characterization theorem , Linear regression , Pareto distribution

Rights: Copyright © 1974 Institute of Mathematical Statistics


Vol.2 • No. 3 • May, 1974
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