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