Abstract
Power-law distributions are widely used 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 using the observed data of interest and then sample from the associated distribution. This approach has important limitations because it relies on a fixed (e.g., it has limited applicability in testing the 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 ) and by showing how additional constraints can be imposed in the sequence (e.g., the Markov transition probability between states). This nonparametric 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 . We test our results in simulated and real data, ranging from the intensity of earthquakes to the number of fatalities in disasters.
- Received 25 June 2021
- Revised 12 March 2022
- Accepted 17 May 2022
DOI:https://doi.org/10.1103/PhysRevX.12.021056
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
Power laws appear widely in physics, biology, Earth science, economics, finance, and social science. They have been used to mathematically describe areas consumed by wildfire, the number of people affected by blackouts, and fatalities from epidemics, wars, and terrorist attacks. These processes can suddenly exhibit extreme events, violating an intuition for how things change that has been developed from interacting with more mundane quantities such as lunch times, lengths of queues, and food prices. The power-law model can be used to predict, prevent, and manage the risk of extremes, but established methods have concerning limitations. Here, we present a strategy to avoid traditional pitfalls.
The shortcoming of established methods for applying a power-law model is that they require unrealistic restrictions. First, they do not apply a general power-law model, but the single specific model that happens to provide the best statistical fit to observations. Second, at odds with human experience, they require processes to be completely without memory.
Our contribution avoids these concerns with a new and theoretically supported approach that involves randomly redistributing observed prime factors. With this tactic, we can apply an unrestricted power-law model while also accommodating any hypothesized memory. Our technique overcomes biases observed with the usual approach and increases model robustness, thus providing better tools to predict, prevent, and manage extreme adverse outcomes.
Substantial research and practical decisions have been based on analysis using established methods for applying power laws, and our work will give researchers and decision makers the opportunity to revisit earlier work with new theoretical support. We hope that our approach will also be useful in completely new studies of power-law processes.
