Scaling distributions and income maximization

Abstract

Judged by the illustrations, this chapter is an exercise in something close to linear programming. The formulas show that this exercise is carried out in a random context ruled by scaling distributions, including the Pareto law for the distribution of personal income. To help both concepts become “broken in” and better understood, I inves?tigated this and other standard topics afresh with the Gaussian replaced by the scaling distribution. For many issues, major “qualitative” changes follow. As is often the case, the root reason lies in sharp contrast in the convexity of probability isolines, between the circles of the form “ x ² + y ² = constant, ” which characterize independent Gaussian coordinates, and the hyperbolas of the form “ xy = constant, ” which characterize independent scaling coordinates. The resulting changes concern an issue central to this book and especially in Chapter E5: evenness of distribution associated with the Gaussian, versus concentration associated with the scaling.