# Book:Charalambos Charalambides/Discrete q-Distributions

## Charalambos Charalambides: Discrete q-Distributions

Published $2016$, Wiley

ISBN 9781119119043.

### Contents

Preface
1 Basic $q$-Combinatorics and $q$-Hypergeometric Series
1.1 Introduction
1.2 $q$-Factorials and $q$-Binomial Coefficients
1.3 $q$-Vandermonde's and $q$-Cauchy's Formulae
1.4 $q$-Binomial and Negative $q$-Binomial Formulae
1.5 General $q$-Binomial Formula and $q$-Exponential Functions
1.6 $q$-Stirling Numbers
1.7 Generalized $q$-Factorial Coefficients
1.8 $q$-Factorial and $q$-Binomial Moments
1.9 Reference Notes
1.10 Exercises
2 Success Probability Varying with the Number of Trials
2.1 $q$-Binomial Distribution of the First Kind
2.2 Negative $q$-Binomial Distribution of the First Kind
2.3 Heine Distribution
2.4 Heine Stochastic Process
2.5 $q$-Stirling Distributions of the First Kind
2.6 Reference Notes
2.7 Exercises
3 Success Probability Varying with Number of Successes
3.1 Negative $q$-Binomial Distribution of the Second Kind
3.2 $q$-Binomial Distribution of the Second Kind
3.3 Euler Distribution
3.4 Euler Stochastic Process
3.5 $q$-Logarithmic Distribution
3.6 $q$-Stirling Distributions of the Second Kind
3.7 Reference Notes
3.8 Exercises
4 Success Probability Varying with the Number of Trials and the Number of Successes
4.1 $q$-Pólya Distribution
4.2 $q$-Hypergeometric Distributions
4.3 Inverse $q$-Pólya Distribution
4.4 Inverse $q$-Hypergeometric Distribution
4.5 Generalized $q$-Factorial Coefficient Distributions
4.6 Reference Notes
4.7 Exercises
5 Limiting Distributions
5.1 Introduction
5.2 Stochastic and in Distribution Convergence
5.3 Laws of Large Numbers
5.4 Central Limit Theorems
5.5 Stieltjes-Wigert Distributions as Limiting Distribution
5.6 Reference Notes
5.7 Exercises
Appendix Hints and Answers to Exercises
References
Index