On the generalized Zipf distribution. Part I

This article is concerned with a class of informetric distribution, a family of skew distributions found to describe a wide range of phenomena both within or outside of information sciences and referred to as being of Zipf-type. A generalization of Zipf distribution (a size-frequency form of the Zipf's law), named the generalized Zipf distribution, is introduced. Two main characterizations of the generalized Zipf distribution are obtained based on the proportionate hazard rate and truncated moments. Finally, some asymptotic properties of the generalized Zipf distribution are investigated.