Statistical models for frequency distributions of count data with applications to scientometrics

This thesis investigates the statistical modelling of count data, common in diverse fields, including bibliometrics and scientometrics. The item production model approach reviews existing models, such as the power law and the generalised inverse Gaussian-Poisson model. Furthermore, a new generalised power law model is proposed to enhance the fitting of models to specific data types. The main focus of the study is on scientific production use cases, encompassing authors, papers, and citations. The research adopts probabilistic combinatorics and the theory of random integer partitions to gain valuable insights into the data structure, which examines Young diagrams and their scaling limits. These insights are then applied to model and estimate production metrics, including the h-index and g-index.