Gini index

Suppose we have a discrete random variable $X$ that can take values in $\{1, 2, \ldots, k\}$. We define the Gini index of $X$ to be

$$Gini(X) = 1 - \sum_{i=1}^k \mathbb{P}(X = i)^2.$$

The higher the entropy the closer to a uniform the random variable we are. $Gini(X) \in [0,\frac{k-1}{k}]$.