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Lorenz Asymmetry Coefficient


The Lorenz asymmetry coefficient is a summary statistic of the Lorenz curve that measures the degree of asymmetry of a Lorenz curve. The Lorenz asymmetry coefficient is defined as

 S=F(mu)+L(mu),
(1)

where the functions F and L are defined as for the Lorenz curve. 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.

The sample statistic S can be calculated from ordered size data using the following equations

delta=(mu-x_m^')/(x_(m+1)^'-x_m^')
(2)
F(mu)=(m+delta)/n
(3)
L(mu)=(L_m+deltax_(m+1)^')/(L_n),
(4)

where m is the number of individuals with a size less than mu.


See also

Gini Coefficient, Lorenz Curve

This entry contributed by Christian Damgaard

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References

Damgaard, C. and Weiner, J. "Describing Inequality in Plant Size or Fecundity." Ecology 81, 1139-1142, 2000.

Referenced on Wolfram|Alpha

Lorenz Asymmetry Coefficient

Cite this as:

Damgaard, Christian. "Lorenz Asymmetry Coefficient." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/LorenzAsymmetryCoefficient.html

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