Gini Coefficient
The Gini coefficient (or Gini ratio) 
is a summary statistic
of the Lorenz curve and a measure of inequality in
a population. The Gini coefficient is most easily calculated from unordered size
data as the "relative mean difference," i.e., the mean of the difference
between every possible pair of individuals, divided by the mean size 
,
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(Dixon et al. 1987, Damgaard and Weiner 2000). Alternatively, if the data is ordered by increasing size of individuals, 
is given by
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(Dixon et al. 1988, Damgaard and Weiner 2000), correcting the typographical error in the denominator given in the original paper (Dixon et al. 1987).
The Gini coefficient ranges from a minimum value of zero, when all individuals are equal, to a theoretical maximum of one in an infinite population in which every individual
except one has a size of zero. It has been shown that the sample Gini coefficients
defined above need to be multiplied by 
in order
to become unbiased estimators for the population
coefficients.
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gini coefficient