GINI - Gini Coefficient

Returns the sample Gini coefficient, a measure of statistical dispersion.

Syntax

Gini(X)

X

is the input data sample (must be non-negative) (a one-dimensional array of cells (e.g., rows or columns)).

Remarks

1. A low Gini coefficient indicates a more equal distribution, with 0 corresponding to complete equality. While higher Gini coefficients indicate more unequal distributions, with 1 corresponding to complete inequality.
2. The input data series may include missing values (e.g., #N/A, #VALUE!, #NUM!, empty cell), but they will not be included in the calculations.
3. The values in the input data series must be non-negative.
4. The Gini coefficient is computed as follows: $$G(S)=1-\frac{2}{n-1}\left ( n-\frac{\sum_{i=1}^{n}iy_i}{\sum_{i=1}^{n}y_i} \right )$$ Where:
   • $h$ is the input data series ($h$) arranged in descending order, so that $y_i\leq y_{i+1}$.
   • $n$ is the number of non-missing values in the input time series data sample.
5. The Gini coefficient value can range from 0 to 1 and is half the relative mean difference (RMD).
6. $G(S)$ is a consistent estimator of the population Gini coefficient but is generally unbiased (except when the population mean is known).
7. Developed by the Italian statistician Corrado Gini in 1912, the Gini coefficient is commonly used as a measure of comparative income or wealth. Where zero (0) corresponds to complete equality and one (1) to complete equality.

Files Examples

Related Links

• Wikipedia - Gini Coefficient.

References

• Hamilton, J .D.; Time Series Analysis, Princeton University Press (1994), ISBN 0-691-04289-6.
• Tsay, Ruey S.; Analysis of Financial Time Series John Wiley & SONS. (2005), ISBN 0-471-690740.