Calculation of maximum entropy densities with application to income distribution

The maximum entropy approach is a flexible and powerful tool for density approximation. This paper proposes a sequential updating method to calculate the maximum entropy density subject to known moment constraints. Instead of imposing the moment constraints simultaneously, the sequential updating method incorporates the moment constraints into the calculation from lower to higher moments and updates the density estimates sequentially. The proposed method is employed to approximate the size distribution of U.S. family income. Empirical evidence demonstrates the efficiency of this method.