Methods of Measuring the Concentration of Wealth

By M. Lorenz. 1905

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A Unified Approach to Quantifying Algorithmic Unfairness: Measuring Individual &Group Unfairness via Inequality Indices (2018, background): “The Gini index has an intuitive interpretation in terms of the Lorenz curve [30], but it does not satisfy an additional property (namely, decomposability) important for our purposes in this work.”
A new model of income distribution: the κ-generalized distribution (2011, unknown): “2.3 Lorenz curve and inequality measures The Lorenz (1905) curve of the κ-generalized distribution is available in terms of the first-moment distribution L(F(x)) = m−1 ∫ x0 x ′ p(x ′) d x ′, namely Lκ(u) = 1 − 1 + κ α 2Γ ( 1 α ) Γ ( 1 2κ + 12α ) Γ ( 1 2κ − 12α ) { 2α(2κ) 1 α (1 − u) [ logκ ( 1 1 −…”
Milestones in the history of thematic cartography, statistica l graphics, and data visualization (2008, unknown): “[160].”
WEALTH INEQUALITY: A SURVEY (2015, unknown): “An additional tool – of tremendous importance – that can be derived from (3) is the wealth share (or Lorenz ordinate) L(F ; q) := C(F ; q) µ(F ) (5) and the associated (relative) Lorenz curve (Lorenz 1905) which is simply the graph10 {(q, L(F ; q)) : 0 ≤ q ≤ 1} .”
Incentive compatible allocation and exchange of discrete resources (2015, unknown): “We compare the equitability of the mechanisms using the equity ranking introduced by Lorenz (1905).38 The outcomes of employees depend of course on the profile of their preferences, and in particular the comparison of the equitability of the mechanisms depends on the preference profile.”
Quantile functions for multivariate analysis: approaches and applications (2002, background): “Initially popular- ized by LORENZ (1905) in the context of income distributions, the Lorenz curve of a positive univariate random variable Y having cdf G is defined as LG( p) ¼ 1 E(Y) ð p 0 G 1(t) dt ¼ 1 E(Y) ðG 1( p) 0 y dG(y), 0 O pO 1: (7) Here LG( p) represents the proportion of total…”
Fairness in Wireless Networks:Issues, Measures and Challenges (2014, methodology): “• Measures of variability such as Lorenz curve and Gini coefficient can be used since they have the ability to reflect distribution gap [18], [19].”
Measuring Resource Inequality: The Gini Coefficient (2009, methodology): “Thus, 2The Lorenz curve is named after Max Otto Lorenz, an American economist who published the idea in 1905 to describe income inequality (Lorenz 1905).”
Frontiers of Stochastically Nondominated Portfolios (2003, background): “The integral in (16) is called the absolute Lorenz curve and is frequently used (for nonnegative variables and in a normalized form) in income inequality studies (see [2, 8, 16, 21, 24] and the references therein).”
Modeling Concentration and Dispersion in Multiple Regression (2005, background): “The Lorenz curve (LC) ( )L u is defined (Lorenz (1905)) to be the proportion of the total amount of income that is owned by the “poorest” 100 × u percent of the population.”
Corporations and economic inequality around the world: The paradox of hierarchy☆ (2010, background): “The Lorenz curve (Lorenz, 1905) is a graphical representation of cumulative income share on the vertical axis and the distribution of the population on the horizontal axis.”
Stochastic Process Methods with an Application to Budgetary Data (2011, background): “Early applications of this approach include the study of income and inequality (Engel 1857; Pareto 1897; Lorenz 1905).”