  Power-law distributions are typical macroscopic features occurring in almost
all complex systems observable in nature. As a result, researchers in
quantitative analyses must often generate random synthetic variates obeying
power-law distributions. The task is usually performed through standard methods
that map uniform random variates into the desired probability space. Whereas
all these algorithms are theoretically solid, in this paper we show that they
are subject to severe machine-dependent limitations. As a result, two dramatic
consequences arise: (i) the sampling in the tail of the distribution is not
random but deterministic; (ii) the moments of the sample distribution, which
are theoretically expected to diverge as functions of the sample sizes,
converge instead to finite values. We provide quantitative indications for the
range of distribution parameters that can be safely handled by standard
libraries used in computational analyses. Whereas our findings indicate
possible reinterpretations of numerical results obtained through flawed
sampling methodologies, they also pave the way for the search for a concrete
solution to this central issue shared by all quantitative sciences dealing with
complexity.
