Book:Charalambos Charalambides/Discrete q-Distributions

{{ #if: |{{{2}}}|Charalambos Charalambides}}{{#if: |{{#if: |, [[Mathematician:{{{author2}}}|{{ #if: |{{{2}}}|{{{author2}}}}}]]{{#if: |, [[Mathematician:{{{author3}}}|{{ #if: |{{{2}}}|{{{author3}}}}}]]{{#if: |, [[Mathematician:{{{author4}}}|{{ #if: |{{{2}}}|{{{author4}}}}}]]{{#if: |, [[Mathematician:{{{author5}}}|{{ #if: |{{{2}}}|{{{author5}}}}}]] and [[Mathematician:{{{author6}}}|{{ #if: |{{{2}}}|{{{author6}}}}}]]| and [[Mathematician:{{{author5}}}|{{ #if: |{{{2}}}|{{{author5}}}}}]]}}| and [[Mathematician:{{{author4}}}|{{ #if: |{{{2}}}|{{{author4}}}}}]]}}| and [[Mathematician:{{{author3}}}|{{ #if: |{{{2}}}|{{{author3}}}}}]]}}| and [[Mathematician:{{{author2}}}|{{ #if: |{{{2}}}|{{{author2}}}}}]]}}}}: {{#if: |[{{{link}}} Discrete q-Distributions]|Discrete q-Distributions}}{{#if: |, Volume {{{volume}}}}}{{#if: | ({{{ed}}} Edition)}}

{{#if: 2016 |Published {{#if: |${{{day}}}$ {{{month}}} ${{{year}}}$|{{#if: |{{{month}}} ${{{year}}}$|{{#if: |c. ${{{circa}}}$|$2016$}}}}}}{{#if: | {{{era}}}|}}{{#if: Wiley |, Wiley{{#if: 9781119119043|: ISBN 9781119119043}}}}{{#if: | (translated by [[Mathematician:{{{translated}}}|{{ #if: |{{{2}}}|{{{translated}}}}}]])}}.}}{{#if: |
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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