{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/non-parametric-power-law-surrogates","title":"Non-parametric power-law surrogates","arxiv_id":"2205.00219","date":"2022-04-30","proceeding":null,"authors":["Jack Murdoch Moore","Gang Yan","Eduardo G. Altmann"],"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.","url_abs":"https://arxiv.org/abs/2205.00219v1","url_pdf":"https://arxiv.org/pdf/2205.00219v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"non-parametric-power-law-surrogates","repo_url":"https://github.com/jackmurdochmoore/power-law","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}