Graphical representation of the distribution of income or of wealth
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A typical Lorenz curve
In economics, the Lorenz curve is a graphical representation of the distribution of income or of wealth. It was developed by Max O. Lorenz in 1905 for representing inequality of the wealth distribution.
The curve is a graph showing the proportion of overall income or wealth assumed by the bottom x% of the people, although this is not rigorously true for a finite population (see below). It is often used to represent income distribution, where it shows for the bottom x% of households, what percentage (y%) of the total income they have. The percentage of households is plotted on the x-axis, the percentage of income on the y-axis. It can also be used to show distribution of assets. In such use, many economists consider it to be a measure of social inequality.
The concept is useful in describing inequality among the size of individuals in ecology[1] and in studies of biodiversity, where the cumulative proportion of species is plotted against the cumulative proportion of individuals.[2] It is also useful in business modeling: e.g., in consumer finance, to measure the actual percentage y% of delinquencies attributable to the x% of people with worst risk scores. Lorenz curves were also applied to epidemiology and public health, e.g., to measure pandemic inequality as the distribution of national cumulative incidence (y%) generated by the population residing in areas (x%) ranked with respect to their local epidemic attack rate.[3]
^Damgaard, Christian; Jacob Weiner (2000). "Describing inequality in plant size or fecundity". Ecology. 81 (4): 1139–1142. doi:10.1890/0012-9658(2000)081[1139:DIIPSO]2.0.CO;2.
^Wittebolle, Lieven; et al. (2009). "Initial community evenness favours functionality under selective stress". Nature. 458 (7238): 623–626. Bibcode:2009Natur.458..623W. doi:10.1038/nature07840. PMID 19270679. S2CID 4419280.
^Nguyen, Quang D.; Chang, Sheryl L.; Jamerlan, Christina M.; Prokopenko, Mikhail (2023). "Measuring unequal distribution of pandemic severity across census years, variants of concern and interventions". Population Health Metrics. 21 (17): 17. doi:10.1186/s12963-023-00318-6. PMC 10613397. PMID 37899455.
economics, the Lorenzcurve is a graphical representation of the distribution of income or of wealth. It was developed by Max O. Lorenz in 1905 for representing...
The Gini coefficient is usually defined mathematically based on the Lorenzcurve, which plots the proportion of the total income of the population (y-axis)...
general rule. The Lorenzcurve is often used to characterize income and wealth distributions. For any distribution, the Lorenzcurve L(F) is written in...
based on the difference between the Lorenzcurve and the value of perfect income equality distribution. The LorenzCurve is a visual representation of income...
income inequality. The Lorenzcurve was taken up by the American statistician Max Lorenz to study the income problem. In the Lorenzcurve method, firstly, the...
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The Lorenz asymmetry coefficient (LAC) is a summary statistic of the Lorenzcurve that measures the degree of asymmetry of the curve. The Lorenzcurve is...
Lorentz curve may refer to the Cauchy–Lorentz distribution, a probability distribution the Lorenzcurve, a graphical representation of the inequality...
distribution sizes. It is used in conjunction with the Lorenzcurve. Originally, the Lorenzcurve measured the inequality of income distributed with a population...
coefficient, the Suits index is calculated by comparing the area under the Lorenzcurve to the area under a proportional line. For a progressive tax (for example...
coefficient is more intuitive to many people since it is based on the Lorenzcurve. However, it is not easily decomposable like the Theil. In addition to...
often inverse relationship. The Lorenzcurve can represent the distribution of income within a society. The Lorenzcurve is closely associated with measures...
approach is constructing a LorenzCurve, a graphical representation of the cumulative percentages of income recipients. The curve compares the actual income...
x_{\textrm {median}}(F_{\kappa })=\beta ^{-1}\ln _{\kappa }(2)} The Lorenzcurve associated with the κ-exponential distribution of type II is given by:...
poorest 20%. Gini Gini index, a quantified representation of a nation's Lorenzcurve. A Gini index of 0% expresses perfect equality, while index of 100% expresses...
Trouble with the Curve is a 2012 American sports drama film directed by Robert Lorenz and starring Clint Eastwood, Amy Adams, Justin Timberlake, Matthew...
Software: Free Online Calculator computes the Gini Coefficient, plots the Lorenzcurve, and computes many other measures of concentration for any dataset Free...
monopolies (via the Herfindahl-Hirschman Index), or in epidemiology where the Lorenzcurve from economics is used to analyze the concentration of risk in a population...
Max Lorenz may refer to: Max Lorenz (tenor) Max Lorenz (footballer) Max O. Lorenz, American economist, responsible for the Lorenzcurve Max Lorentz, Swedish...
makes credit inexpensive and abundant, possibly leading to inflation. Lorenzcurve loss aversion Lucas critique Lucas paradox Lundberg lag luxury good macroeconomic...
consumption, rather than income or wealth. Asset Economic inequality Income Lorenzcurve Wealth concentration Wealth (economics) Wealth https://www.oecd-ilibrary...
HRV), by Dr. Egon Winter, Austria. Accessed 2016-11-20. In German. 'LorenzCurve' command in online user manual for 'Dataplot' software, published by...
coefficient Hoover index (a.k.a. Robin Hood index) Income inequality metrics Lorenzcurve Rényi entropy Suits index Theil index Shorrocks, A. F. (1980). "The Class...
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