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Power-law probability distributions arise often in the social and naturalsciences. Statistics have been developed for estimating the exponent parameteras well as gauging goodness-of-fit to a power law. Yet paradoxically, manyfamous power laws such as the distribution of wealth and earthquake magnitudeshave not found good statistical support in data by modern methods. We show thatmeasurement errors such as quantization and noise bias both maximum-likelihoodestimators and goodness-of-fit measures. We address this issue usinglogarithmic binning and the corresponding discrete reference distribution formaximum likelihood estimators and Kolmogorov-Smirnov statistics. Usingsimulated errors, we validate that binning attenuates bias in parameterestimates and recalibrates goodness of fit to a power law by removing smallerrors from consideration. These benefits come at modest cost in statisticalpower, which can be compensated with larger sample sizes. We reanalyse threeempirical cases of wealth, earthquake magnitudes and wildfire area and showthat binning reverses statistical conclusions and aligns the statisticalresults with historical and scientific expectations. We explain through thesecases how routine errors lead to incorrect conclusions and the necessity formore robust methods.

Tunable robustness in power-law inference