Calculation of maximum entropy densities with application to income distribution

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GMM estimation of a maximum entropy distribution with interval data (2007, background): “( )( )0 1log[ exp ]M i ii g xθ == −∑∫ Zellner and Highfield (1988) and Wu (2003) discuss the estimation of maxent density subject to moment constraints for the entire distribution.”
The size distribution of US cities: Not Pareto, even in the tail (2013, methodology): “From standard limiting theory, the llr test is asymptotically χ21 and is optimal (Cox and Hinkley, 1974; Wu, 2003).6 The ME test is a by-product of a more general non-parametric approach to density estimation.”
Models for Time-varying Moments Using Maximum Entropy Applied to a Generalized Measure of Volatility (2008, unknown): “3Compare Wu (2003).”
China's Income Distribution, 19852001 (2005, unknown): “Traditionally, this maximum entropy density can be obtained by maximizing Shannon’s information entropy ( ) ( )logW p x p x dx= −∫ subject to K known moment conditions for the entire range of the distribution ( ) ( ) ( ) 1, 1,2,..., .i i p x dx g x p x dx i Kμ = = , = ∫ ∫ 7 We can solve this optimiz”
More than Mean Effects: Modeling the Effect of Climate on the Higher Order Moments of Crop Yields (2012, unknown): “To estimate the univariate maximum entropy distributions, we utilize the sequential updating method developed in Wu (2003).”