  The prevailing maximum likelihood estimators for inferring power law models
from rank-frequency data are biased. The source of this bias is an
inappropriate likelihood function. The correct likelihood function is derived
and shown to be computationally intractable. A more computationally efficient
method of approximate Bayesian computation (ABC) is explored. This method is
shown to have less bias for data generated from idealised rank-frequency
Zipfian distributions. However, the existing estimators and the ABC estimator
described here assume that words are drawn from a simple probability
distribution, while language is a much more complex process. We show that this
false assumption leads to continued biases when applying any of these methods
to natural language to estimate Zipf exponents. We recommend that researchers
be aware of these biases when investigating power laws in rank-frequency data.
