Turing--Entropic Tail Classification: A Nonparametric Approach to Tail Inference
This article introduces the Turing--Entropic Tail Classifier (TENT), a nonparametric information-theoretic framework for tail inference in discrete and continuous distributions. Central to the approach is the tail profile, a collection of information-theoretic quantities motivated by Turing's formula and domain-of-attraction theory on countable alphabets. TENT classifies the qualitative form of tail decay by comparing empirical tail profiles with theoretical benchmarks corresponding to exponential-type, near-exponential, sub-exponential, and power-law regimes, including Zipf and Pareto-type behavior. For heavier-than-exponential tails, the framework further yields point and interval estimates for selected tail parameters. Although the method is primarily designed to support preliminary model selection for discrete parametric families, a supporting result shows that, under suitable regularity conditions, discretizing continuous observations by common-width binning preserves the relevant tail decay rate. This provides a principled route for extending the classifier to continuous data. Simulation studies illustrate the finite-sample performance of TENT across multiple tail classes and sampling regimes.