Use of Hazard Functions for Determining Power-Law Behaviour in Data

Determining the ‘best-fitting’ distribution for data is an important problem in data analysis. Specifically, observing how the distribution of data changes as values below (or above) a threshold are omitted from analyses can be of use in various applications, from animal movement to the modelling of natural phenomena. Such truncated distributions, known as hazard functions, are widely studied and well understood in survival analysis, although rarely widely used in data analysis. Here, by considering the hazard and reverse-hazard functions, we demonstrate a qualitative assessment of the ‘best-fit’ distribution of data. Specifically, we highlight the potential advantages of this method when determining whether power-law behaviour may or may not be present in data. Finally, we demonstrate this approach using some real-world datasets.