Charalambos A. Charalambides, PhD, is Professor Emeritus in the Department of Mathematics at the University of Athens, Greece. An elected member of the International Statistical Institute, his research interests include enumerative combinatorics, combinatorial probability, and parametric inference/point estimation. He is the author of Combinatorial Methods of Discrete Distributions, also published by Wiley.

• Preface ix1 Basicq-combinatorics and q-hypergeometric series 11.1 Introduction 11.2 q-Factorials and q-binomial coefficients 21.3 q-Vandermonde’s and q-Cauchy’s formulae 101.4 q-Binomial and negative q-binomial formulae 161.5 General q-binomial formula and q-exponential functions 241.6 q-Stirling numbers 261.7 Generalized q-factorial coefficients 361.8 q-Factorial and q-binomial moments 421.9 Reference notes 451.10 Exercises 462 Success probability varying with the number of trials 612.1 q-binomial distribution of the first kind 612.2 Negative q-binomial distribution of the first kind 662.3 Heine distribution 692.4 Heine stochastic process 732.5 q-Stirling distributions of the first kind 772.6 Reference notes 852.7 Exercises 863 Success probability varying with the number of successes 973.1 Negative q-binomial distribution of the second kind 973.2 q-Binomial distribution of the second kind 1023.3 Euler distribution 1053.4 Euler stochastic process 1093.5 q-Logarithmic distribution 1143.6 q-Stirling distributions of the second kind 1173.7 Reference notes 1223.8 Exercises 1234 Success probability varying with the number of successes and the number of trials 1354.1 q-Pólya distribution 1354.2 q-Hypergeometric distributions 1444.3 Inverse q-pólya distribution 1504.4 Inverse q-hypergeometric distributions 1544.5 Generalized q-factorial coefficient distributions 1554.6 Reference notes 1644.7 Exercises 1655 Limiting distributions 1735.1 Introduction 1735.2 Stochastic and in distribution convergence 1745.3 Laws of large numbers 1765.4 Central limit theorems 1815.5 Stieltjes–wigert distribution as limiting distribution 1855.6 Reference notes 1935.7 Exercises 193Appendix Hints and answers to exercises 197References 235Index 241

"The book is interesting, and ought to be useful for all researchers in the developing area of discrete distribution theory. It is also an ideal and comprehensive textbook for graduate level courses in distribution theory and enumerative combinatorics" Malvina George Vamvakari, Mathematical Reviews, Sept 2017