Figure 6
Bias in ABC (solid blue) vs Clauset et al.’s estimator (dashed red) for unbounded power laws. For each of 100 values of \(\lambda\) between 1.01 and 2, rank-frequency data (\(N=\)10,000) was generated by sampling an unbounded power law. This was run 100 times. The left figure shows the known \(\lambda\) and the mean estimated \(\lambda\). The centre figure shows the mean bias, with a 68\(\%\) confidence interval shaded. The right figure shows the variance of the estimators. The ABC estimator has much lower bias and similar variance to Clauset et al.’s estimator.
