RELATIVE DISTRIBUTION METHODS


                Mark S. Handcock
             Department of Statistics
            Pennsylvania State University



The relative distribution is a tool for the comparative
analysis of distributional differences between a comparison
and reference distribution.  It is the random variable
obtained by transforming a comparison random variable by
the cumulative distribution function (CDF) of a reference
random variable.  The corresponding density and CDF
are being used by social scientists and economists to
represent interdistributional dissimilarity.

Methods based on the relative distribution combine the
graphical tools of exploratory data analysis with a
framework for statistical decomposition and inference.
The analytic framework is general and flexible, as the
relative density is decomposable into the effect of
location and shape differences, and into effects that
represent both compositional changes in covariates, and
changes in the covariate-outcome variable relationship.

In this seminar we discuss the statistical estimation
of, and inference for, the relative CDF and relative
density.  We also we discuss the statistical properties
of median, lower and upper relative polarization indices.
They numerically measure a key characteristic of the
relative distribution, namely the amount of polarization
or divergence.

The methods are illustrated by the study of the pattern
of US income inequality over time.