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Power-law distributions contain precious information about a large variety ofprocesses in geoscience and elsewhere. Although there are sound theoreticalgrounds for these distributions, the empirical evidence in favor of power lawshas been traditionally weak. Recently, Clauset et al. have proposed asystematic method to find over which range (if any) a certain distributionbehaves as a power law. However, their method has been found to fail, in thesense that true (simulated) power-law tails are not recognized as such in someinstances, and then the power-law hypothesis is rejected. Moreover, the methoddoes not work well when extended to power-law distributions with an uppertruncation. We explain in detail a similar but alternative procedure, valid fortruncated as well as for non-truncated power-law distributions, based inmaximum likelihood estimation, the Kolmogorov-Smirnov goodness-of-fit test, andMonte Carlo simulations. An overview of the main concepts as well as a recipefor their practical implementation is provided. The performance of our methodis put to test on several empirical data which were previously analyzed withless systematic approaches. The databases presented here include the half-livesof the radionuclides, the seismic moment of earthquakes in the whole world andin Southern California, a proxy for the energy dissipated by tropical cycloneselsewhere, the area burned by forest fires in Italy, and the waiting timescalculated over different spatial subdivisions of Southern California. We findthe functioning of the method very satisfactory.

Fitting and goodness-of-fit test of non-truncated and truncated power-law distributions