Zipfʹs law, hyperbolic distributions and entropy loss

Zipfʹs law – or Estoup-Zipfʹs law – is an empirical fact of computational linguistics which relates rank and frequency of words in natural languages. The law suggests modelling by distributions of “hyperbolic type”. We present a satisfactory general definition and an information theoretical characterization of the resulting hyperbolic distributions. When applied to linguistics this leads to a property of stability and flexibility, explaining that a language can develop towards higher and higher expressive powers without changing its basic structure.