| Three essays are addressed in the thesis. Traditionally, descriptive tools such as the Gini index and Lorenz curve are used in the study of income distribution. However, we can rely on statitiscal inference for ranking income distribution. Not only does statistical inference take into account sample variability, but it also changes qualitatively the nature of the conclusions and allows more conclusions. In essay I we will address this issue by comparing recently developed statistical ranking of income distributions with the traditional numeric ranking of income distributions.;In essay 2, we will assess the quality of statistical hypothesis tests for ranking income distributions by bootstrap resampling. A significant difference between statistical inference and bootstrapping is found for small sample size. The difference is insignificant when sample size becomes large. We also examine Type I and Type II errors for statistical ranking and study their sensitivity by sample size and significance.;In essay 3, the statistical ranking techniques are used to study the convergence of regional income distributions. The study shows that the U.S. South and non-South income distributions were converging by the criteria of rank dominance and generalized Lorenz dominance between the fifties and seventies, but were diverging in the eighties. |
