Why Some Powers Laws Are Possible And Some Are Not

Authors

Edgar Daniel Rodriguez Velasquez, Universidad de PiuraFollow
Vladik Kreinovich, The University of Texas at El PasoFollow
Olga Kosheleva, The University of Texas at El PasoFollow
Nguyen Hoang Phuong, Thang Long UniversityFollow

Publication Date

5-2020

Comments

Technical Report: UTEP-CS-20-47

Abstract

Many dependencies between quantities are described by power laws, in which y is proportional to x raised to some power a. In some application areas, in different situations, we observe all possible pairs (A,a) of the coefficient of proportionality A and of the exponent a. In other application areas, however, not all combinations (A,a) are possible: once we fix the coefficient A, it uniquely determines the exponent a. In such case, the dependence of a on A is usually described by an empirical logarithmic formula. In this paper, we show that natural scale-invariance ideas lead to a theoretical explanation for this empirical formula.