Intensity and shape of inequalities: The ABG method for the analysis of distributions

Inequality is anisotropic: its intensity is variable along the income scale. Therefore, to focus on local inequalities, a new representation, the isograph, is developed to figure their variations. This leads to the expression of three coefficients able to summarize the shape of inequalities: a main coefficient, alpha, measures inequality at the median, and two correction coefficients, beta and gamma, take into account the curvatures at the top and at the bottom of the distribution. A set of 212 samples of microdata surveys from 40 different countries of the LIS datacenter archive provides a systematic view on the properties of these ABG (alpha beta gamma) coefficients that are compared to a set of standard indices (Atkinson indexes, generalized entropy, Wolfson polarization, etc.). This method also provides a smoothing tool that is able to show the differences in shape of distributions (strobiloid) and their change over time.