  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.
