Analysis of power-law exponents by maximum-likelihood maps

TL;DR

This paper evaluates maximum-likelihood exponent maps as a method to better understand and fit power-law exponents in data with cut-offs, through applications to seismology, acoustic emissions, and simulations.

Contribution

It demonstrates the effectiveness of maximum-likelihood exponent maps in analyzing complex power-law data with cut-offs across different physical systems.

Findings

Exponent maps reveal deviations in power-law fits.

The technique improves understanding of physical phenomena.

Applications include seismology and material failure simulations.

Abstract

Maximum-likelihood exponent maps have been studied as a technique to increase the understanding and improve the fit of power-law exponents to experimental and numerical simulation data, especially when they exhibit both upper and lower cut-offs. The use of the technique is tested by analyzing seismological data, acoustic emission data and avalanches in numerical simulations of the 3D-Random Field Ising model. In the different examples we discuss the nature of the deviations observed in the exponent maps and some relevant conclusions are drawn for the physics behind each phenomenon.