Lower Bound of Gini Index for Mixed Distribution--- with Results for China with Urban-Rural DualisticStructure

This paper studies the lower bound of the Gini index for the mixed distribution of two distributions with certain weights by grouped data. These results are used to calculate the Gini index for China with urban-rural dualistic structure. They could be expanded to mixed distributions with more than two sub-distributions and could be used to other real situations, such as union of countries or areas.