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→Lorenz curve and Gini coefficient
[[Derek J.de Solla Price#科学贡献| Price的平方根定律]]有时作为帕累托分布的属性或类似于帕累托分布提供。然而，该定律只适用于<math>\alpha=1</math>的情况。请注意，在这种情况下，没有定义财富的总量和预期金额，而且该规则只适用于渐近随机样本。上面提到的扩展帕累托原则是一个更一般的规则。
[[Derek J.de Solla Price#科学贡献| Price的平方根定律]]有时作为帕累托分布的属性或类似于帕累托分布提供。然而，该定律只适用于<math>\alpha=1</math>的情况。请注意，在这种情况下，没有定义财富的总量和预期金额，而且该规则只适用于渐近随机样本。上面提到的扩展帕累托原则是一个更一般的规则。
===Lorenz curve and Gini coefficient===
===Lorenz curve and Gini coefficient洛伦兹曲线与基尼系数===
| title=Ecrits sur la courbe de la répartition de la richesse
| title=Ecrits sur la courbe de la répartition de la richesse
|关于财富分配曲线的文章
| title=Ecrits sur la courbe de la répartition de la richesse
| title=Ecrits sur la courbe de la répartition de la richesse
|财富分配曲线上的文字
[[File:ParetoLorenzSVG.svg|thumb|325px|Lorenz curves for a number of Pareto distributions. The case ''α'' = ∞ corresponds to perfectly equal distribution (''G'' = 0) and the ''α'' = 1 line corresponds to complete inequality (''G'' = 1)]]
[[File:ParetoLorenzSVG.svg|thumb|325px|Lorenz curves for a number of Pareto distributions. The case ''α'' = ∞ corresponds to perfectly equal distribution (''G'' = 0) and the ''α'' = 1 line corresponds to complete inequality (''G'' = 1)]]
[[文件：ParetoLorenzSVG.svg|许多帕累托分布的拇指| 325px |洛伦兹曲线。情形“α”== ；∞对应于完全相等分布（“G”= ；0），而“α”==1行对应于完全不等式（“G”= ；1)]]
| first=Vilfredo
| first=Vilfredo
The [[Lorenz curve]] is often used to characterize income and wealth distributions. For any distribution, the Lorenz curve ''L''(''F'') is written in terms of the PDF ''f'' or the CDF ''F'' as
The [[Lorenz curve]] is often used to characterize income and wealth distributions. For any distribution, the Lorenz curve ''L''(''F'') is written in terms of the PDF ''f'' or the CDF ''F'' as
[[Lorenz曲线]]通常用于描述收入和财富分配。对于任何分布，洛伦兹曲线“L”（“F”）用PDF“F”或CDF“F”表示为
| editor=Librairie Droz
| editor=Librairie Droz
For <math>0<\alpha\le 1</math> the denominator is infinite, yielding ''L''=0. Examples of the Lorenz curve for a number of Pareto distributions are shown in the graph on the right.
For <math>0<\alpha\le 1</math> the denominator is infinite, yielding ''L''=0. Examples of the Lorenz curve for a number of Pareto distributions are shown in the graph on the right.
对于<math>0<\alpha\le 1</math>分母是无穷大的，得到“L”=0。右图显示了一些Pareto分布的Lorenz曲线示例。
| doi=10.1177/000271629700900314| s2cid=143528002
| doi=10.1177/000271629700900314| s2cid=143528002
According to [[Oxfam]] (2016) the richest 62 people have as much wealth as the poorest half of the world's population.<ref>{{cite web|title=62 people own the same as half the world, reveals Oxfam Davos report|url=https://www.oxfam.org/en/pressroom/pressreleases/2016-01-18/62-people-own-same-half-world-reveals-oxfam-davos-report|publisher=Oxfam|date=Jan 2016}}</ref> We can estimate the Pareto index that would apply to this situation. Letting ε equal <math>62/(7\times 10^9)</math> we have:
According to [[Oxfam]] (2016) the richest 62 people have as much wealth as the poorest half of the world's population.<ref>{{cite web|title=62 people own the same as half the world, reveals Oxfam Davos report|url=https://www.oxfam.org/en/pressroom/pressreleases/2016-01-18/62-people-own-same-half-world-reveals-oxfam-davos-report|publisher=Oxfam|date=Jan 2016}}</ref> We can estimate the Pareto index that would apply to this situation. Letting ε equal <math>62/(7\times 10^9)</math> we have:
根据[[Oxfam]]（2016年），最富有的62人拥有的财富与世界上最贫穷的一半人口的财富相同。<ref>{cite web | title=62人拥有的财富与世界上一半的人相同，展示乐施会达沃斯报告网址=https://www.oxfam.org/en/pressroom/pressreases/2016-01-18/62-people-own-same-half-world-reviews-oxfam-davos-report|publisher=Oxfam | date=2016年1月}</ref>我们可以估计适用于这种情况的帕累托指数。让ε等于<math>62/（7乘以10^9）</math>我们得到：
:<math>L(1/2)=1-L(1-\varepsilon)</math>
:<math>L(1/2)=1-L(1-\varepsilon)</math>