Numerical method to calculate Gini coefficient from limited data of subgroups

A numerical method is proposed to calculate the income distribution and Gini coefficient of the total population from the limited data of subgroups. The method is optimized to simulate the Lorenz curve of each subgroup with the third spline interpolation, and the cumulative income distribution curve of each subgroup and the total population is calculated. Thus the Lorenz curve of the total population can be predicted to obtain the Gini coefficient. The method can simulate the complex income distribution with a relative error of less than 4%. It overcomes the defect of the present method with a function to simulate the complex income distribution of subgroup such as the multiple peaks which will introduce much more error.