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 
.
