In economics and social sciences, inequality measures such as Gini index, Peitra index etc., are commonly used to measure the evenness of probability distributions. In this paper, we first review some entropy maximization studies under moment and inequality measures constraints. Next, we consider a generalization of Gini index and based on the principle of maximum-entropy we find the probability distribution that maximizes the entropy among all probability distributions supported on non-negative real values with a given mean and a given generalized Gini index.

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