Power-law distributions in binned empirical data
| Autor: | Yogesh Virkar, Aaron Clauset |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2014 |
| Předmět: |
FOS: Computer and information sciences
Statistics and Probability Physics - Physics and Society model selection Computer science Population FOS: Physical sciences Physics and Society (physics.soc-ph) heavy-tailed distributions Statistics - Applications binned data Statistical power Methodology (stat.ME) symbols.namesake Power-law distribution Statistics Applications (stat.AP) Pareto distribution education Statistics - Methodology Statistic Statistical hypothesis testing education.field_of_study Model selection Empirical distribution function Heavy-tailed distribution Physics - Data Analysis Statistics and Probability Modeling and Simulation symbols Statistics Probability and Uncertainty Data Analysis Statistics and Probability (physics.data-an) |
| Zdroj: | Ann. Appl. Stat. 8, no. 1 (2014), 89-119 |
| Popis: | Many man-made and natural phenomena, including the intensity of earthquakes, population of cities and size of international wars, are believed to follow power-law distributions. The accurate identification of power-law patterns has significant consequences for correctly understanding and modeling complex systems. However, statistical evidence for or against the power-law hypothesis is complicated by large fluctuations in the empirical distribution's tail, and these are worsened when information is lost from binning the data. We adapt the statistically principled framework for testing the power-law hypothesis, developed by Clauset, Shalizi and Newman, to the case of binned data. This approach includes maximum-likelihood fitting, a hypothesis test based on the Kolmogorov--Smirnov goodness-of-fit statistic and likelihood ratio tests for comparing against alternative explanations. We evaluate the effectiveness of these methods on synthetic binned data with known structure, quantify the loss of statistical power due to binning, and apply the methods to twelve real-world binned data sets with heavy-tailed patterns. Comment: Published in at http://dx.doi.org/10.1214/13-AOAS710 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org) |
| Databáze: | OpenAIRE |
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