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Preface ix
1 Basic q-combinatorics and q-hypergeometric series 1
1.1 Introduction 1
1.2 q-Factorials and q-binomial coefficients 1
1.3 q-Vandermonde’s and q-Cauchy’s formulae 10
1.4 q-Binomial and negative q-binomial formulae 16
1.5 General q-binomial formula and q-exponential functions 24
1.6 q-Stirling numbers 26
1.7 Generalized q-factorial coefficients 36
1.8 q-Factorial and q-binomial moments 42
1.9 Reference notes 44
1.10 Exercises 45
2 Success probability varying with the number of trials 61
2.1 q-Binomial distribution of the first kind 61
2.2 Negative q-binomial distribution of the first kind 66
2.3 Heine distribution 69
2.4 Heine stochastic process 73
2.5 q-Stirling distributions of the first kind 77
2.6 Reference notes 84
2.7 Exercises 85
3 Success probability varying with the number of successes 95
3.1 Negative q-binomial distribution of the second kind 95
3.2 q-Binomial distribution of the second kind 99
3.3 Euler distribution 103
3.4 Euler stochastic process 107
3.5 q-Logarithmic distribution 111
3.6 q-Stirling distributions of the second kind 114
3.7 Reference notes 119
3.8 Exercises 121
4 Success probability varying with the number of successes and the number of trials 131
4.1 q-Pólya distribution 131
4.2 q-Hypergeometric distributions 139
4.3 Inverse q-Pólya distribution 145
4.4 Inverse q-hypergeometric distributions 149
4.5 Generalized q-factorial coefficient distributions 150
4.6 Reference notes 159
4.7 Exercises 160
5 Limiting distributions 167
5.1 Introduction 167
5.2 Stochastic and in distribution convergence 168
5.3 Laws of large numbers 170
5.4 Central limit theorems 175
5.5 Stieltjes-Wigert distribution as limiting distribution 179
5.6 Reference notes 186
5.7 Exercises 186
Appendix Hints and answers to exercises 191
Bibliography 229
Index 233
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Discrete q-distributions by Ch. A. Charalambides. ISBN 9781119119104. Published by John Wiley & Sons, Inc. in 2016. Publication and catalogue information, links to buy online and reader comments.