The Third Edition of the critically acclaimed Univariate Discrete Distributions addresses the latest advances in discrete distributions theory. New distributions, including q-series and generalized zeta-function distributions, are explored in detail. New families of distributions, including Lagrangian-type distributions, have been integrated into this thoroughly revised and updated text. In addition, new applications of univariate discrete distributions, including sports applications, have been added to demonstrate the flexibility of this powerful method. Throughout the Third Edition, extensive information has been added to reflect the new role of computer-based applications. With its thorough coverage and balanced presentation of theory and application, this is an excellent graduate-level textbook and essential reference for statisticians and mathematicians.