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Figure 1

From: Bias in Zipf’s law estimators

Figure 1

Bias in maximum likelihood estimation for rank-frequency data. 100 values of \(\lambda\) between 1 and 2 were investigated. For each \(\lambda\), samples with \(N=100,000\) were generated from an unbounded power law distribution and Clauset et al.’s estimator was applied to the empirical rank-frequency distribution. This was repeated 100 times and results averaged. There is a clear and strong positive bias for \(\lambda \lessapprox 1.5\).

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