The most important indicator for measuring income inequality is the Gini index. The Gini index summarizes an entire income distribution and overall degree of income inequality but have little to say about information the distribution of income between the different classes of income and the Lorenz curve. For example, when asymmetric cases that the Gini indexes for two different Lorenz curves are identical using the Gini index of income inequality alone, it is not clear that the increases in income inequality have been due to the rich getting richer or the poor become poorer. Therefore, this indicator may not be characterized as all changes in income concentration. To solve this problem, there are methods and indicators. At first, in this paper has been discussed approaches of several researchers to solve this problem by the application of skewness of Lorentz curve and then proposed a skewness coefficient as the best representation of the changes in the extremes. As an application example, the income distribution of provinces in particular for two provinces Khuzestan and Hormozgan in 2008, stressing that the two provinces are the same Gini coefficient has been examined.