Some Properties of Zipf’s Law and Applications

Abstract

The article extends the theoretical and applicative analysis of Zipf’s law. We are concerned with a set of properties of Zipf’s law that derive directly from the power law expression and from the discrete nature of the objects to which the law is applied, when the objects are words, lemmas, and the like. We also search for variations of Zipf’s law that can help explain the noisy results empirically reported in the literature and the departures of the empirically obtained nonlinear graph from the theoretical linear one, with the variants analyzed differing from Mandelbrot and lognormal distributions. A problem of interest that we deal with is that of mixtures of populations obeying Zipf’s law. The last problem has relevance in the analysis of texts with words with various etymologies. Computational aspects are also addressed.