# Universality of power-law exponents by means of maximum likelihood estimation

## TL;DR

This paper introduces a statistical method to merge datasets for better power-law analysis, demonstrating its effectiveness on earthquake data and labquakes, revealing universal exponents across different systems.

## Contribution

The paper presents a novel statistical procedure to combine datasets, enabling more accurate power-law exponent estimation over broader ranges in complex systems.

## Key findings

- Merged earthquake catalogs show a power-law over eight orders of magnitude.
- The exponent of labquake energy distribution varies with material.
- Earthquake and labquake data share the same power-law exponent.

## Abstract

Power-law type distributions are extensively found when studying the behaviour of many complex systems. However, due to limitations in data acquisition, empirical datasets often only cover a narrow range of observation, making it difficult to establish power-law behaviour unambiguously. In this work we present a statistical procedure to merge different datasets with the aim of obtaining a broader fitting range for the statistics of different experiments or observations of the same system or the same universality class. This procedure is applied to the Gutenberg-Richter law for earthquakes and for synthetic earthquakes (acoustic emission events) generated in the laboratory: labquakes. Different earthquake catalogs have been merged finding a Gutenberg-Ricther law holding for more than eight orders of magnitude in seismic moment. The value of the exponent of the energy distribution of labquakes depends on the material used in the compression experiments. By means of the procedure exposed in this manuscript, it has been found that the Gutenberg-Richter law for earthquakes and charcoal labquakes can be characterized by the same power-law exponent.