This work is a comprehensive introduction to the statistical analysis of word frequency distributions, intended for computational linguists, corpus linguists, psycholinguists, and researchers in the field of quantitative stylistics. Word frequency distributions are characterized by very large numbers of rare words. This property leads to strange phenomena such as mean frequencies that systematically change as the number of observations is increased, relative frequencies that even in large samples are not fully reliable estimators of population probabilities, and model parameters that vary with text or corpus size. Special statistical techniques for the analysis of distributions with large numbers of rare events can be found in various technical journals. The aim of this book is to make these techniques more accessible for non-specialists, both theoretically, by means of a careful introduction to the underlying probabilistic and statistical concepts, and practically, by providing a program library implementing the main models for word frequency distributions.