Gini-coefficient, a widely used measure of inequality in income is defined as :
1
\( \frac{1}{\mathrm{n}^2 \mu} \sum_i^{\mathrm{n}} \sum_{j \leq 1}\left(y_i-y_j\right) \)
2
\( \frac{2}{\mathrm{n}^2 \mu} \sum_i^{\mathrm{n}} i y_i-\left[\frac{\mathrm{n}+1}{\mathrm{n}}\right] \)
3
\( \frac{2}{\mathrm{n} \mu} \frac{\sum_i^{\mathrm{n}} i y_i}{\sum_i^{\mathrm{n}} y_i}-\left[\frac{\mathrm{n}+1}{\mathrm{n}}\right] \)
4
\( \frac{1}{\mathrm{n}^2 \mu} \sum_{i=1}^{\mathrm{n}} \sum_{j=1}^{\mathrm{n}}\left|\left(y_i-y_j\right)\right| \)