Quantile Tool Box Measures for Empirical Analysis and for Testing Distributional Comparisons in Direct Distribution-Free Fashion

This paper provides a set of tool box measures for flexibly describing distributional changes and empirically implementing several dominance criteria for social welfare comparisons and broad income inequality comparisons. Dominance criteria are expressed in terms of vectors of quantile statistics based on income shares and quantile means. Asymptotic variances and covariances of these sample ordinates are established from a Quantile Function Approach that provides a framework for direct statistical inference on these vectors. And practical empirical criteria are forwarded for using formal statistical inference tests to reach conclusions about ranking social welfare and inequality between distributions. Examples include rank dominance, Lorenz dominance, generalized Lorenz dominance, income polarization, and distributional distance dominance between income groups.