Mathematical modeling using partition theory and data compression

Abstract

This paper provides additional insight and information about a newly described method and mathematical model which is created by using number theory and a lossless data compression technique. The central tenet of this method and model suggests a strong connection between additive number theory (partitions) and statistics-in that, it shows how a scatterplot or a set of data, if modeled as a finite binary string, can be 'classified' using partition theory. Secondly, this method contributes the idea of using partitions as a model from which objective probabilities are derived-thus, linking the concept of statistics with data compression via partition theory. In the context of this method and model, a third important idea emerges-in which, a set of data or a scatterplot is converted into a unique real number (called a CADAMA number) which can be plotted and used for the purpose of storing and retrieving the original set of data, data analysis, and can potentially enhance or guide the decision-making process of a decision-maker. Finally, this method and model provides an opportunity to further validate, reexamine, and refine some of the fundamental first principles in statistics from a number theoretic point of view.