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Abstract In this paper, instead of likelihood based methods that are fragile under model uncertainty, we use entropy based methods on time-ordered household income data to recover income distribution information on European countries and obtain an inequality income measure. For information recovery, we use a family of information theoretic entropy divergence measures to obtain income probability density functions and the corresponding inequality measures, which reflect how European country based economic behavioral systems are performing, and in terms of dynamics have changed over time. Highlights • Information Theoretic Entropy recovery methods. • Income probability distributions of micro income data for 16 European countries. • Alternative to likelihood based methods that are fragile under model uncertainty. • Derive the implied measure of inequality for each country. [ABSTRACT FROM AUTHOR]

In this paper, we focus on the first significant digit (FSD) distribution of European micro income data and use information theoretic-entropy based methods to investigate the degree to which Benford’s FSD law is consistent with the nature of these economic behavioral systems. We demonstrate that Benford’s law is not an empirical phenomenon that occurs only in important distributions in physical statistics, but that it also arises in self-organizing dynamic economic behavioral systems. The empirical likelihood member of the minimum divergence-entropy family, is used to recover country based income FSD probability density functions and to demonstrate the implications of using a Benford prior reference distribution in economic behavioral system information recovery. [ABSTRACT FROM AUTHOR]