The x-axis records the cumulative proportion of some population (people, rabbits, defective widgets etc.)
ranked by the cumulative proportion of an associated y-measure (income, births, cost of repairs, etc.).
It is therefore, a square plot with (0,1) ranges.
To reproduce the "augmented" Lorenz curve (Figure 2) in this paper by Kunegis and Preusse, "Fairness on the Web: Alternatives to the Power Law" in WebSci 2012, June 22–24, 2012, Evanston, Illinois, USA::
Figure 2. Statistics associated with the Pareto principle. [...]The Lorenz curve (continuous line) gives rise to two statistics: The Gini coefficient G is twice the gray area and the balanced inequality ratio P is the point at which the antidiagonal crosses the Lorenz curve.
The 'the balanced inequality ratio P' that Kunegis and Preusse identify is typically used in a statement echoing the Pareto principle, e.g.: P% of all <users/objects> account for X% of all <some measures/resources...>.
The area below the diagonal is equal to half the total area of the square;
It is also equal to the area between the diagonal and the Lorenz curve = A,
plus what's left = B.
Therefore, the Gini coefficient, G is: G = A/(A+B)
Since A+B = 0.5, G = 2A
You can view the code in ./lgp_curve/LorenzGiniP.py.
The Lorenz_Gini_P_curve notebook has the coding details (imports, calls, etc.).
The Gini ratio was calculated using interpolation and integration: it will likely not be equal to the analyticaly calculated ratio; my guesstimate for the discrepancy is 0.05 to 0.1.
- python 3.
- numpy
- scipy (for .integrate.trapz)
- pandas
- matplotlib
- Refine plotting function to pass style dict for plot text
- Refine plotting function to pass style dict for figure save options.
- Check discrepancy of Gini value viz analytical solution