Discrete q-distributions. (2016)
- Record Type:
- Book
- Title:
- Discrete q-distributions. (2016)
- Main Title:
- Discrete q-distributions
- Further Information:
- Note: Charalambos A. Charalambides.
- Authors:
- Charalambides, Ch. A
- Contents:
- 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 5.1Preface 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 … (more)
- Edition:
- 1st
- Publisher Details:
- Hoboken, New Jersey : John Wiley & Sons, Inc
- Publication Date:
- 2016
- Extent:
- 1 online resource
- Subjects:
- 519.24
Distribution (Probability theory)
Stochastic sequences
Discrete geometry
Combinatorial geometry - Languages:
- English
- ISBNs:
- 9781119119104
- Related ISBNs:
- 9781119119043
- Notes:
- Note: Includes bibliographical references and index.
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- British Library HMNTS - ELD.DS.48670
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