Distinguishing between a power law and a Pareto distribution

This paper introduces the location Pareto distribution as a natural extension of the power law distribution and gives a likelihood ratio test for choosing between the two models. Some properties of the distribution and test are thoroughly investigated, and applications to real data are provided. For large values of the observations the two models perform similarly; this explains why some classical approaches are very insensitive to the differentiation between them. The likelihood ratio test between the two models is simple to use and has a high level of discrimination power. It is recommended when the complementary cumulative distribution function exhibits linearity on a log-log scale.

Automated summary

This paper introduces the location Pareto distribution as an extension of the power law distribution and provides a likelihood ratio test for model selection. The properties of the distribution and test are thoroughly investigated, and real data applications are presented. For large observations, the two models perform similarly, explaining why classical approaches are insensitive to differentiating between them. The recommended likelihood ratio test is simple and has high discrimination power when the complementary cumulative distribution function exhibits linearity on a log-log scale.