Pennsylvania State University - Department of Statistics
The relative distribution is a non-parametric complete summary of the information required for scale-invariant comparisons between two distributions. It can be used to represent interdistributional dissimilarity in location, scale, and other factors. The relative distribution is defined as the transformation of a variable from a comparison group by the cumulative distribution function (CDF) of that variable for a reference group. In this seminar we describe an analytic framework for the relative distribution that integrates graphical techniques, decomposition methods, and summary measures. We discuss inference for the relative CDF, the relative density, and relative polarization indices. The relative density and CDF are beginning to be used by social scientists to represent and analyze distributional differences, enabling researchers to move well beyond comparisons of means and variances in a simple intuitive way. We illustrate the use of the methods with applications to recent trends in inequality and wage mobility in the United States.