The maximal value of a zipf size variable: Sampling properties and relationship to other parameters

摘要

Because the Zipf size-frequency distribution is used so often as a mathematical model for bibliometric variables, it is important that the relationships among its parameters and its sampling properties be understood by investigators in this field. This paper examines these relationships and properties. In addition, it provides tables for the sampling distribution of the maximal value of a finite Zipf distribution and an approximation formula for confidence intervals. Confidence limits for the maximal value in a number of previous studies are determined.