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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Lorenz asymmetry coefficient ： ウィキペディア英語版 Lorenz asymmetry coefficient The Lorenz asymmetry coefficient (LAC) is a summary statistic of the Lorenz curve that measures the degree of asymmetry of the curve. The Lorenz curve is used to describe the inequality in the distribution of a quantity (usually income or wealth in economics, or size or reproductive output in ecology). The most common summary statistic for the Lorenz curve is the Gini coefficient, which is an overall measure of inequality within the population. The Lorenz asymmetry coefficient can be a useful supplement to the Gini coefficient. The Lorenz asymmetry coefficient is defined as :$S\; =\; F(\backslash mu)+\; L(\backslash mu)\backslash ,$ where the functions ''F'' and ''L'' are defined as for the Lorenz curve, and ''μ'' is the mean. If ''S'' > 1, then the point where the Lorenz curve is parallel with the line of equality is above the axis of symmetry. Correspondingly, if ''S'' < 1, then the point where the Lorenz curve is parallel to the line of equality is below the axis of symmetry. If data arise from the log-normal distribution, then ''S'' = 1, i.e., the Lorenz curve is symmetric.〔Damgaard & Weiner (2000)〕 The sample statistic ''S'' can be calculated from ''n'' ordered size data, $(x\_1,\; ...,\; x\_m,x\_,...,\; x\_n)$, using the following equations: :$\backslash delta=\backslash frac$ :$F(\backslash mu)=\backslash frac$ :$L(\backslash mu)=\backslash frac$, where ''m'' is the number of individuals with a size or wealth less than ''μ''〔 and $L\_i=\backslash sum\_^i\; x\_j$ The Lorenz asymmetry coefficient characterizes an important aspect of the shape of a Lorenz curve. It tells which size or wealth classes contribute most to the population’s total inequality, as measured by the Gini coefficient. If the LAC is less than 1, the inequality is primarily due to the relatively many small or poor individuals. If the LAC is greater than 1, the inequality is primarily due to the few largest or wealthiest individuals. For incomes distributed according to a log-normal distribution, the LAC is identically 1. ==Notes== 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「Lorenz asymmetry coefficient」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.