New classes of Lorenz curves by maximizing Tsallis entropy under mean and Gini equality and inequality constraints

•The Tsallis entropy measure is used to construct new Lorenz curves for modeling income distribution.•The maximum entropy principle is used, under mean and Gini index equality and inequality constraints.•The entropic approach enables deriving maximal entropy Lorenz curves with mean and Gini index constraints.•The inequality constraints approach is new and more realistic, since it allows a greater degree of flexibility.•The paper extends recent results obtained in this field.

In this paper, by using the entropy maximization principle with Tsallis entropy, new distribution families for modeling the income distribution are derived. Also, new classes of Lorenz curves are obtained by applying the entropy maximization principle with Tsallis entropy, under mean and Gini index equality and inequality constraints.