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 $\alpha$ 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 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 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 $\alpha$. We test our results in simulated and real data, ranging from the intensity of earthquakes to the number of fatalities in disasters.

中文翻译：

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非参数幂律代理

幂律分布广泛用于极端事件和复杂系统的计算和统计调查。生成幂律分布数据的常用技术是首先推断尺度指数$\alpha$使用观察到的感兴趣的数据，然后从相关分布中采样。这种方法有很大的局限性，因为它依赖于一个固定的$\alpha$（例如，它在检验幂律分布族方面的适用性有限）和独立观察假设（例如，它忽略了复杂系统数据中通常存在的时间相关性和其他约束）。在这里，我们提出了一种约束代理方法，它通过从一组序列中随机均匀地选择，与原始序列在离散幂律下观察到的可能性完全相同（即，无论$\alpha$) 并通过展示如何在序列中施加额外的约束（例如，状态之间的马尔可夫转移概率）。这种非参数方法涉及重新分配观察到的主要因素以根据幂律模型随机化值，但不限于独立观察或特定$\alpha$. 我们在模拟和真实数据中测试我们的结果，从地震强度到灾难中的死亡人数。