Why Burr Distribution: Invariance-Based Explanation

Author:

Velasquez Edgar Daniel Rodriguez12,Thach Nguyen Ngoc3

Affiliation:

1. Department of Civil Engineering, Universidad de Piura in Peru (UDEP), Av. Ramon Mugica 131, Piura, Peru

2. Department of Civil Engineering, University of Texas at El Paso, 500 W. University, El Paso, Texas 79968, USA

3. Ho Chi Minh University of Banking, 36 Ton That Dam, District 1, Ho Chi Minh City, Vietnam

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.

Publisher

World Scientific Pub Co Pte Ltd

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1. Guest Editorial: Uncertainty in Economics and Finance;International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems;2023-12

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