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Chapter 5. Growth Dynamics
Figure 5.3: Lorenz curve for Out-Degree Count in Spring framework in
release 2.5.3.
is a curve of perfect inequality.
For a probability density function f (x) and cumulative density function
F(x), the Lorenz curve L(F(x)) is defined as:
L(F(x)) =
∫ x
−∞
t f (t) dt
∫ ∞
−∞ t f (t) dt (5.2.1)
The Lorenz curve can be used to measure the distribution of functionality
within a system. Figure 5.3 is a Lorenz curve for the Fan-Out Count
metric in the Spring framework release 2.5.3. Although the Lorenz
curve does capture the nature of distribution, it can be summarized
more effectively by means of the Gini coefficient. The Gini coefficient is
defined as a ratio of the areas on the Lorenz curve diagram. If the area
between the line of perfect equality and Lorenz curve is A, and the area
under the Lorenz curve is B, then the Gini coefficient is A/(A + B) [311].
More formally, if the Lorenz curve is L(Y), then the Gini Coefficient is
defined as:
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