Generalizations of power-law distributions applicable to sampled fault-trace lengths: model choice, parameter estimation and caveats

It has often been observed that fault-trace lengths tend to follow a power-law or Pareto distribution, at least for suciently large lengths. A very common method of tting this type of model to data consists of plotting on log^log axes the number of faults with trace length greater than x against x, and reading o the slope of the resulting approximate straight line. We demonstrate that maximum likelihood is a more ecient and less biased method of estimating the power-law exponent.