Why Burr Distribution: Invariance-Based Explanation

Abstract

In many practical situations, we observe a special Burr probability distribution — e.g., Burr distribution describes the distribution of people by income, it describes the rainfall data, etc. In this paper, we provide a theoretical explanation for the ubiquity of Burr distributions: namely, we show that this distribution naturally follows from scale-invariance. To be more precise, the simplest distribution that can be obtained from scale invariance is the Pareto distribution — a frequent particular case of the general Burr family of distributions. Next simplest are all distributions from the Burr family. We also use the scale-invariance approach to come up with a more general class of distributions that will, hopefully, provide an even more accurate description of the corresponding phenomena.