A complete data frame work for fitting power law distributions

Over the last few decades power law distributions have been suggested as forming generative mechanisms in a variety of disparate fields, such as, astrophysics, criminology and database curation. However, fitting these heavy tailed distributions requires care, especially since the power law behaviour may only be present in the distributional tail. Current state of the art methods for fitting these models rely on estimating the cut-off parameter $x_{\min}$. This results in the majority of collected data being discarded. This paper provides an alternative, principled approached for fitting heavy tailed distributions. By directly modelling the deviation from the power law distribution, we can fit and compare a variety of competing models in a single unified framework.