A Unified Approach to Economic Dominance and Inequality Measures using a General Transformation Function

We present three generalized, empirical, economic inequality definitions for the empirical dominance of the income distribution of Population 1 over that of Population 2 with respect to their n-person economy in terms of a general transformation function G. These definitions are based on the generalized gaps using the general G function instead of the standard gaps, to achieve greater flexibility and higher generality in performing many comparisions between Populations 1 and 2, in terms of the mean as well as the variance, geometric mean, median, and range. This article provides a unified approach to various dominance concepts and inequality measures. This unification is achieved through the transformation function G. We study the effects of the economic inequality definitions on location and dispersion of the income distribution. Log-normal, log-skew-normal, and Pareto distributions are considered in this study.