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

(1)

where the functions  and  are defined as for the Lorenz curve. If , then the point where the Lorenz curve is parallel with the line of equality is above the axis of symmetry. Correspondingly, if , then the point where the Lorenz curve is parallel to the line of equality is below the axis of symmetry.

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

			(2)
			(3)
			(4)

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

REFERENCES:

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