Probability-turbulence divergence: A tunable allotaxonometric instrument for comparing heavy-tailed categorical distributions

Understand

Real-world complex systems often comprise many distinct types of elements as well as many more types of networked interactions between elements.

• When the relative abundances of types can be measured well, we often observe heavy-tailed categorical distributions for type frequencies.
• For the comparison of type frequency distributions of two systems or a system with itself at different time points in time -- a facet of allotaxonometry -- a great range of probability divergences are available.
• Here, we introduce and explore `probability-turbulence divergence', a tunable, straightforward, and interpretable instrument for comparing normalizable categorical frequency distributions.