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In the last years, researchers have realized the difficulties of fittingpower-law distributions properly. These difficulties are higher in Zipf'ssystems, due to the discreteness of the variables and to the existence of tworepresentations for these systems, i.e., two versions about which is the randomvariable to fit. The discreteness implies that a power law in one of therepresentations is not a power law in the other, and vice versa. We generatesynthetic power laws in both representations and apply a state-of-the-artfitting method (based on maximum-likelihood plus a goodness-of-fit test) foreach of the two random variables. It is important to stress that the methoddoes not fit the whole distribution, but the tail, understood as the part of adistribution above a cut-off that separates non-power-law behavior frompower-law behavior. We find that, no matter which random variable is power-lawdistributed, the rank-size representation is not adequate for fitting, whereasthe representation in terms of the distribution of sizes leads to the recoveryof the simulated exponents, may be with some bias.

The distinct flavors of Zipf's law in the rank-size and in the size-distribution representations, and its maximum-likelihood fitting