Nonparametric Power-Law Surrogates

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 α using the observed data of interest and then sample from the associated distribution. This approach has important limitations because it relies on a fixed α (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 α) 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 α. We test our results in simulated and real data, ranging from the intensity of earthquakes to the number of fatalities in disasters.