| Lorenz Curve and Gini Coefficient |
| See Also |
This menu allows you to plot Lorenz curves and calculate the Gini coefficient
of inequality. The Lorenz curve provides a graphical representation of the inequality of a
sample of numbers. In economics the numbers could be the annual incomes of
a group of people, or in ecology they could be population sizes of a set of
species of animal or plant. The y-coefficients for the curve are formed by
sorting the numbers, calculating their cumulative totals, and then dividing
these by the grand total. The x-coefficients are simply the numbers 0, 1,
... n, where n is the size of the sample. If the numbers are all equal,
the curve will form a straight line, known as the line of equality, running
from the origin to the point (1, 1). Inequalities amongst the numbers cause
the curve to lie below the line of equality.
The Gini coefficient is the area between the line of equality and the Lorenz
curve area, divided by area under the line of equality. So, a value close to
zero indicates near equality, while a value near to one shows a high amount of
inequality. The asymmetry coefficient assesses the amount of asymmetry of the
Lorenz curve. The axis of symmetry for the curve is the line from (1, 0) to
(0, 1). The coefficient is less than one if the point where the Lorenz curve
is parallel to the line of equality lies below the axis of symmetry, and
greater than one if it lies above the axis.
Data
A variate containing the data whose equality is to be studied.
Available Data
This lists data structures appropriate to the current input field. The contents will change as you move from one field to the
next. Double-click on a name to copy it to the current input field; alternatively, you can type the name directly into the input field.
Graphics
Specifies the plots to be displayed.
| Lorenz curve | Plots the Lorenz curve. |
Display
Specifies the output to be displayed.
| Gini coefficient | Displays the Gini coefficient and confidence interval (if selected). |
| Coefficient of asymmetry | Displays the coefficient of asymmetry and confidence interval (if selected). |
| Lorenz curve coordinates | Displays coordinates of the Lorenz curve. |
Include Confidence Interval
| Confidence Limit (%) | Specifies the confidence limit as a percentage. |
| Number of samples of bootstrap | Specifies the number of samples used in the bootstrap. |
| Seed | Specifies the seed to use in the random number generator used to
construct the bootstrap samples. The default value of zero continues
an existing sequence of random numbers or, if the generator has not yet been
used in this run of GenStat, it initializes the generator automatically. |
See Also