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