Why Quadratic Log-Log Dependence Is Ubiquitous And What Next

Authors

Sean R. Aguilar, The University of Texas at El PasoFollow
Vladik Kreinovich, The University of Texas at El PasoFollow
Uyen Pham, University of Economics and LawFollow

Publication Date

7-2020

Comments

Technical Report: UTEP-CS-20-75

To appear in Asian Journal of Economics and Banking (AJEB)

Abstract

In many real-life situations ranging from financial to volcanic data, growth is described either by a power law -- which is linear in log-log scale, or by a quadratic dependence in the log-log scale. In this paper, we use natural scale invariance requirement to explain the ubiquity of such dependencies. We also explain what should be a reasonable choice of the next model, if quadratic turns out to be not too accurate: it turns out that under scale invariance, the next class of models are cubic dependencies in the log-log scale, then fourth order dependencies, etc.