Pareto's law | ScienceGate

The problem of estimating the exponent of a stable law is receiving an increasing amount of attention because Pareto's law (or Zipf's law) describes many biological phenomena very well (see e.g. Hill (1974)). This problem was first solved by Hill (1975), who proposed an estimate, and the convergence of that estimate to some positive and finite number was shown to be a characteristic of distribution functions belonging to the Fréchet domain of attraction (Mason (1982)). As a contribution to a complete theory of inference for the upper tail of a general distribution function, we give the asymptotic behavior (weak and strong) of Hill's estimate when the associated distribution function belongs to the Gumbel domain of attraction. Examples, applications and simulations are given.

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Wealth distribution and Pareto's law in the Hungarian medieval society

Physica A Statistical Mechanics and its Applications ◽

10.1016/j.physa.2007.02.094 ◽

2007 ◽

Vol 380 ◽

pp. 271-277 ◽

Cited By ~ 18

Author(s):

Géza Hegyi ◽

Zoltán Néda ◽

Maria Augusta Santos

Keyword(s):

Wealth Distribution ◽

Pareto’S Law

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A. C. Pigou's rejection of Pareto's law

Cambridge Journal of Economics ◽

10.1093/cje/bes045 ◽

2012 ◽

Vol 37 (4) ◽

pp. 775-789 ◽

Cited By ~ 5

Author(s):

M. McLure

Keyword(s):

Pareto’S Law

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Asymptotic behavior of Hill's estimate and applications

Journal of Applied Probability ◽

10.2307/3214466 ◽

1986 ◽

Vol 23 (4) ◽

pp. 922-936 ◽

Cited By ~ 5

Author(s):

Gane Samb Lo

Keyword(s):

Distribution Function ◽

Asymptotic Behavior ◽

Finite Number ◽

Domain Of Attraction ◽

Distribution Functions ◽

Complete Theory ◽

General Distribution ◽

Stable Law ◽

Biological Phenomena ◽

Pareto’S Law

The problem of estimating the exponent of a stable law is receiving an increasing amount of attention because Pareto's law (or Zipf's law) describes many biological phenomena very well (see e.g. Hill (1974)). This problem was first solved by Hill (1975), who proposed an estimate, and the convergence of that estimate to some positive and finite number was shown to be a characteristic of distribution functions belonging to the Fréchet domain of attraction (Mason (1982)). As a contribution to a complete theory of inference for the upper tail of a general distribution function, we give the asymptotic behavior (weak and strong) of Hill's estimate when the associated distribution function belongs to the Gumbel domain of attraction. Examples, applications and simulations are given.

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On Pareto's Law

Journal Of The Royal Statistical Society ◽

10.2307/2980528 ◽

1937 ◽

Vol 100 (3) ◽

pp. 421 ◽

Cited By ~ 7

Author(s):

C. Bresciani-Turroni

Keyword(s):

Pareto’S Law

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Zipf's Law, Pareto's Law, and the Evolution of Top Incomes in the United States

American Economic Journal Macroeconomics ◽

10.1257/mac.20150051 ◽

2017 ◽

Vol 9 (3) ◽

pp. 36-71 ◽

Cited By ~ 15

Author(s):

Shuhei Aoki ◽

Makoto Nirei

Keyword(s):

United States ◽

Income Distribution ◽

The United States ◽

Zipf’S Law ◽

Tax Rates ◽

Firm Level ◽

Productivity Shocks ◽

Zipf's Law ◽

Top Incomes ◽

Pareto’S Law

We construct a tractable neoclassical growth model that generates Pareto's law of income distribution and Zipf's law of the firm size distribution from idiosyncratic, firm-level productivity shocks. Executives and entrepreneurs invest in risk-free assets, as well as their own firms' risky stocks, through which their wealth and income depend on firm-level shocks. By using the model, we evaluate how changes in tax rates can account for the evolution of top incomes in the United States. The model matches the decline in the Pareto exponent of the income distribution and the trend of the top 1 percent income share in recent decades. (JEL D31, H24, L11)

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