On the Truncated Zipf Distribution and Its Structural Properties with Applications

The discrete version of the Pareto distribution, popularly known as the Zipf distribution, and its truncated version are not new in the literature but several structural properties have not yet been discussed, and nor has its application to a wide range of observed phenomena. Here, we refer to the truncated Zipf distribution meaning the Zipf distribution when the support set is finite. Several interesting and useful structural properties of the truncated Zipf distribution, such as the modal dominance bounds, recurrence relation among successive raw moments, and stochastic ordering are thoroughly discussed. To exhibit the flexibility of the assumed probability model, COVID-19 datasets from three different geographical regions have been re-analyzed and are compared with several rival univariate discrete probability models which establishes the superiority of the truncated Zipf distribution.