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Power-law distributions are typical macroscopic features occurring in almostall complex systems observable in nature. As a result, researchers inquantitative analyses must often generate random synthetic variates obeyingpower-law distributions. The task is usually performed through standard methodsthat map uniform random variates into the desired probability space. Whereasall these algorithms are theoretically solid, in this paper we show that theyare subject to severe machine-dependent limitations. As a result, two dramaticconsequences arise: (i) the sampling in the tail of the distribution is notrandom but deterministic; (ii) the moments of the sample distribution, whichare theoretically expected to diverge as functions of the sample sizes,converge instead to finite values. We provide quantitative indications for therange of distribution parameters that can be safely handled by standardlibraries used in computational analyses. Whereas our findings indicatepossible reinterpretations of numerical results obtained through flawedsampling methodologies, they also pave the way for the search for a concretesolution to this central issue shared by all quantitative sciences dealing withcomplexity.

Underestimating extreme events in power-law behavior due to machine-dependent cutoffs