Calculation of maximum entropy densities with application to income distribution

• Published in: Journal of econometrics Vol. 115; no. 2; pp. 347 - 354
• Main Author: Wu, Ximing
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.08.2003; Elsevier; Elsevier Sequoia S.A
• Series: Journal of Econometrics
• Subjects: Applications; Applied sciences; Density estimation; Distribution theory; Econometrics; Economic theory; Entropy; Exact sciences and technology; Family income; Income distribution; Insurance, economics, finance; Inventory control, production control. Distribution; Mathematics; Maximum entropy; Methods; Operational research and scientific management; Operational research. Management science; Probability and statistics; Sciences and techniques of general use; Sequential methods; Sequential updating; Statistics; Studies; U.S.A; United States > US; C4; Density estimation; Income distribution; C6; Sequential updating; Maximum entropy; D3; Statistical method; Statistical moment; Sequential method; Method of maximum entropy; Econometrics
• ISSN: 0304-4076; 1872-6895
• DOI: 10.1016/S0304-4076(03)00114-3

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.