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Why Burr Distribution: Invariance-Based Explanation

Edgar Daniel Rodriguez Velasquez

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

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

E-mail Address: edgar.rodriguez@udep.pe

E-mail Address: edrodriguezvelasquez@miners.utep.edu

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and

Nguyen Ngoc Thach

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

E-mail Address: thachnn@hub.edu.vn

Corresponding author.

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https://doi.org/10.1142/S0218488523400147Cited by:1 (Source: Crossref)

This article is part of the issue:

Special Issue on Uncertainty in Economics and Finance

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.

Keywords:

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