Lorenz asymmetry coefficient
Encyclopedia
The Lorenz asymmetry coefficient is a summary statistic of the Lorenz curve
that measures the degree of asymmetry of the curve. The Lorenz asymmetry coefficient is defined as
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.
The sample statistic S can be calculated from n ordered size data,
, using the following equations:
,
where m is the number of individuals with a size less than μ.
Lorenz curve
In economics, the Lorenz curve is a graphical representation of the cumulative distribution function of the empirical probability distribution of wealth; it is a graph showing the proportion of the distribution assumed by the bottom y% of the values...
that measures the degree of asymmetry of the curve. The Lorenz asymmetry coefficient is defined as
where the functions F and L are defined as for the Lorenz curve
Lorenz curve
In economics, the Lorenz curve is a graphical representation of the cumulative distribution function of the empirical probability distribution of wealth; it is a graph showing the proportion of the distribution assumed by the bottom y% of the values...
, 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.
The sample statistic S can be calculated from n ordered size data,
, using the following equations:,where m is the number of individuals with a size less than μ.
External links
- LORENZ 3.0 is a MathematicaMathematicaMathematica is a computational software program used in scientific, engineering, and mathematical fields and other areas of technical computing...
notebook which draw sample Lorenz curveLorenz curveIn economics, the Lorenz curve is a graphical representation of the cumulative distribution function of the empirical probability distribution of wealth; it is a graph showing the proportion of the distribution assumed by the bottom y% of the values...
s and calculates Gini coefficientGini coefficientThe Gini coefficient is a measure of statistical dispersion developed by the Italian statistician and sociologist Corrado Gini and published in his 1912 paper "Variability and Mutability" ....
s and Lorenz asymmetry coefficients from data in an Excel sheet.