翻訳と辞書 Words near each other ・ Paresk ・ Paressisus viridipennis ・ Paressonodon ・ Paresthesia ・ Parestola ・ Paret ・ Paretak ・ Paretaxalus ・ Parete ・ Pareto ・ Pareto analysis ・ Pareto chart ・ Pareto distribution ・ Pareto efficiency ・ Pareto Group ・ Pareto index ・ Pareto interpolation ・ Pareto Platform ・ Pareto principle ・ Pareto priority index ・ Pareto's law ・ Pareto, Piedmont ・ Paretroplus ・ Paretroplus dambabe ・ Paretroplus gymnopreopercularis ・ Paretroplus lamenabe ・ Paretroplus loisellei ・ Paretroplus maromandia ・ Paretroplus menarambo ・ Paretroplus nourissati Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Pareto index ： ウィキペディア英語版 Pareto index In economics the Pareto index, named after the Italian economist and sociologist Vilfredo Pareto, is a measure of the breadth of income or wealth distribution. It is one of the parameters specifying a Pareto distribution and embodies the Pareto principle. As applied to income, the Pareto principle is sometimes stated in popular expositions by saying 20% of the population has 80% of the income. In fact, Pareto's data on British income taxes in his ''Cours d'économie politique'' indicates that about 20% of the population had about 80% of the income. One of the simplest characterizations of the Pareto distribution, when used to model the distribution of incomes, says that the proportion of the population whose income exceeds any positive number ''x'' > ''x''m is :$\backslash left(\backslash frac\backslash right)^\backslash alpha$ where ''x''m is a positive number, the minimum of the support of this probability distribution (the subscript m stands for ''minimum''). The Pareto index is the parameter α. Since a proportion must be between 0 and 1, inclusive, the index α must be positive, but in order for the total income of the whole population to be finite, α must also be greater than 1. The larger the Pareto index, the smaller the proportion of very high-income people. Given a $p\; +\; q\; =\; 1$ rule, with $p\; >\; q$, the Pareto index is given by: :$\backslash alpha\; =\; \backslash log\_\; 1/q\; =\; \backslash log(1/q)/\backslash log(p/q)\; =\; \backslash log(q)/\backslash log(q/p).$ If $q\; =\; 1/n$, this simplifies to :$\backslash alpha\; =\; \backslash log\_\; (n).$ Alternatively, in terms of odds, X:Y :$\backslash alpha\; =\; \backslash log\_\; (X+Y)/Y,$ so X:1 yields :$\backslash alpha\; =\; \backslash log\_X\; (X+1).$ For example, the 80–20 (4:1) rule corresponds to α = log(5)/log(4) ≈ 1.16, 90–10 (9:1) corresponds to α = log(10)/log(9) ≈ 1.05, and 99–1 corresponds to α = log(10)/log(9) ≈ 1.002, whereas the 70–30 rule corresponds to α = log(0.3)/log(0.3/0.7) ≈ 1.42 and 2:1 (67–33) corresponds to α = log(3)/log(2) ≈ 1.585. Mathematically, the formula above entails that all incomes are at least the lower bound ''x''m, which is positive. At this income the probability density suddenly jumps up from zero and then starts decreasing, which is clearly unrealistic. Economists therefore sometimes state that the Pareto law as stated here applies only to the upper tail of the distribution. == See also == * Gini coefficient * List of measures of inequality 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Pareto index」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.