Hoover Index - Computation

Computation

For the formula, a notation is used, where the amount of quantiles only appears as upper border of summations. Thus, inequities can be computed for quantiles with different widths . For example, could be the income in the quantile #i and could be the amount (absolute or relative) of earners in the quantile #i. then would be the sum of incomes of all quantiles and would be the sum of the income earners in all quantiles.

Computation of the Robin Hood index :

H = {\frac{1}{2}} \sum_{i=1}^N \color{Blue} \left| \color{Black} {\frac{{E}_i}{{E}_\text{total}}} - {\frac{{A}_i}{{A}_\text{total}}} \color{Blue} \right| \color{Black}.

For comparison, here also the computation of the symmetrized Theil index is given:

T_s = {\frac{1}{2}} \sum_{i=1}^N \color{Blue} \ln{\frac{{E}_i}{{A}_i}} \left( \color{Black} {\frac{{E}_i}{{E}_\text{total}}} - {\frac{{A}_i}{{A}_\text{total}}} \color{Blue} \right) \color{Black}.

Both formulas can be used in spreadsheet computations.

Read more about this topic:  Hoover Index

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