Why k-Systems Methodology Works

Abstract

k-Systems methodology takes an arbitrary finite valued multivariate real function and transforms it into a dimensionless (0,1) interval function with associated equations. Computations are then performed on this function and its marginal equations invoking solely the principle of maximum entropy. Many traditional statistical measures are thereby computed in this context. The claim is that this constitutes a correct framework for these measures.This theory has many statisticians throwing up their hands in consternation. The principle of maximum entropy is somewhat mysterious itself, but now the k-systems (0,1) function no longer represents relative frequencies, and the principle of maximum entropy has only been applied and rationalized for relative frequencies. Puzzling questions arise: Just what is this methodology doing, why does it seem to do it so well, and why and when is it correct? In this paper we explore the rationale behind k-systems.