Page 99 - Becoming Metric Wise

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Statistics

Figure 4.13 A Lorenz curve.

equal to twice this area. The Gini index of the diagonal is zero and when
one item takes a larger and larger share of the whole (TOT) the corre-
sponding Gini index becomes closer and closer to one. The formula to
calculate a Gini index of an ordered sequence X 5 (x j ) j of length N is:
!
N
1 2 X
gðXÞ 5 N 1 1 2 jx j (4.19)
N TOT
j51
In most applications outside informetrics (economy, ecology, demog-
raphy), the Lorenz curve is represented as a convex curve, by ranking
data from smallest to largest. If this is done, then the Gini index is calcu-
lated as follows:
!
N
1 2 X
gðXÞ 5 N 1 1 2 ð N 2 j 1 1Þ x j (4.20)
N TOT
j51