Maximum-likelihood fitting of Zipf's law should use the distribution of sizes, not the rank-size relation, because only the former recovers simulated exponents.
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The distinct flavors of Zipf's law in the rank-size and in the size-distribution representations, and its maximum-likelihood fitting
Maximum-likelihood fitting of Zipf's law should use the distribution of sizes, not the rank-size relation, because only the former recovers simulated exponents.