Comparing inequality of distributions on the basis of mixed Lorenz curves

The Lorenz dominance (LD) is generally used to rank Lorenz curves (LCs) or, equivalently, the corresponding distributions, in terms of inequality. When LCs intersect, the LD is not verified, but we can rely on weaker orders such as the upward or downward second-degree Lorenz dominance (2-LD), which emphasize the effect of the left or the right tail, respectively. The main idea of this paper it to propose a dominance relation that lies between the LD and the 2-LD, i.e. weaker than the former and stronger than the latter. For this purpose, we introduce a mixed Lorenz curve, that is, a mix of the original LC and a symmetric trasformation of it. By so doing, our approach is also intended to emphasize both tails of the distribution, rather than one. We provide an exemplification with regard to distributions of income