Non-parametric power-law surrogates

TL;DR

This paper introduces a non-parametric surrogate method for generating power-law distributed data that overcomes limitations of traditional parametric approaches by allowing for arbitrary exponents and temporal correlations.

Contribution

The authors propose a novel non-parametric method to generate power-law surrogates that do not depend on a fixed exponent or independence assumptions, accommodating additional constraints.

Findings

Effective in simulating power-law data with arbitrary exponents

Applicable to real-world data such as earthquakes and disaster fatalities

Preserves temporal correlations and other constraints in surrogate data

Abstract

Power-law distributions are essential in computational and statistical investigations of extreme events and complex systems. The usual technique to generate power-law distributed data is to first infer the scale exponent $\alpha$ using the observed data of interest and then sample from the associated distribution. This approach has important limitations because it relies on a fixed $\alpha$ (e.g., it has limited applicability in testing the {\it family} of power-law distributions) and on the hypothesis of independent observations (e.g., it ignores temporal correlations and other constraints typically present in complex systems data). Here we propose a constrained surrogate method that overcomes these limitations by choosing uniformly at random from a set of sequences exactly as likely to be observed under a discrete power-law as the original sequence (i.e., regardless of $\alpha$) and by showing how additional constraints can be imposed in the sequence (e.g., the Markov transition probability between states). This non-parametric approach involves redistributing observed prime factors to randomize values in accordance with a power-law model but without restricting ourselves to independent observations or to a particular $\alpha$. We test our results in simulated and real data, ranging from the intensity of earthquakes to the number of fatalities in disasters.