  Power-law distributions contain precious information about a large variety of
processes in geoscience and elsewhere. Although there are sound theoretical
grounds for these distributions, the empirical evidence in favor of power laws
has been traditionally weak. Recently, Clauset et al. have proposed a
systematic method to find over which range (if any) a certain distribution
behaves as a power law. However, their method has been found to fail, in the
sense that true (simulated) power-law tails are not recognized as such in some
instances, and then the power-law hypothesis is rejected. Moreover, the method
does not work well when extended to power-law distributions with an upper
truncation. We explain in detail a similar but alternative procedure, valid for
truncated as well as for non-truncated power-law distributions, based in
maximum likelihood estimation, the Kolmogorov-Smirnov goodness-of-fit test, and
Monte Carlo simulations. An overview of the main concepts as well as a recipe
for their practical implementation is provided. The performance of our method
is put to test on several empirical data which were previously analyzed with
less systematic approaches. The databases presented here include the half-lives
of the radionuclides, the seismic moment of earthquakes in the whole world and
in Southern California, a proxy for the energy dissipated by tropical cyclones
elsewhere, the area burned by forest fires in Italy, and the waiting times
calculated over different spatial subdivisions of Southern California. We find
the functioning of the method very satisfactory.
