An Interpolating Family of size distributions
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Power laws and power laws with exponential cut-off are two distinct families of size distributions. In the present paper, we propose a unified treatment of both families by building a family of distributions that interpolates between them, hence the name Interpolating Family (IF) of distributions. Our original construction, which relies on techniques from statistical physics, provides a connection for hitherto unrelated distributions like the Pareto and Weibull distributions, and sheds new light on them. The IF also contains several distributions that are neither of power law nor of power law with exponential cut-off type. We calculate quantile-based properties, moments and modes for the IF. This allows us to review known properties of famous size distributions and to provide in a single sweep these characteristics for various less known (and new) special cases of our Interpolating Family.
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