Why Some Power Laws Are Possible and Some Are Not

Rodriguez Velasquez E.D.; Kreinovich V.; Kosheleva O.; Nguyen H.P. · Studies in Computational Intelligence (2021) · DOI: 10.1007/978-3-030-76620-7_18

Resumen

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.

Instituciones: Universidad de Piura