TY  - BOOK
AU  - Charalambides,Charalambos A.
ED  - SpringerLink (Online service)
TI  - Multivariate Discrete q-Distributions
T2  - Synthesis Lectures on Mathematics & Statistics,
SN  - 9783031437137
AV  - QA297.4 
PY  - 2024///
CY  - Cham
PB  - Springer Nature Switzerland, Imprint: Springer
KW  - Discrete mathematics
KW  - Probabilities
KW  - Mathematics
KW  - Distribution (Probability theory)
KW  - Discrete Mathematics
KW  - Applications of Discrete Mathematics
KW  - Probability Theory
KW  - Applied Probability
KW  - Applications of Mathematics
KW  - Distribution Theory
N1  - Preface -- Multivariate q-Combinatorics and q-Hypergeometric Series -- Multivariate q-Distributions -- Appendix: Hints and Answers to Exercises -- Bibliography -- Index
N2  - This book is devoted to the study of multivariate discrete q-distributions, which is greatly facilitated by existing multivariate q-sequences and q-functions. Classical multivariate discrete distributions are defined on a sequence of independent and identically distributed Bernoulli trials, with either being a success of a certain rank (level) or a failure. The author relaxes the assumption that the probability of success of a trial is constant by assuming that it varies geometrically with the number of trials and/or the number of successes. The latter is advantageous in the sense that it permits incorporating the experience gained from the previous trials and/or successes, which leads to multivariate discrete q-distributions. Furthermore, q-multinomial and negative q-multinomial formulae are obtained. Next, the book addresses q-multinomial and negative q-multinomial distributions of the first and second kind.The author also examines multiple q-Polya urn model, multivariate q-Polya and inverse q-Polya distributions. Presents definitions and theorems that highlight key concepts and worked examples to illustrate the various applications Contains numerous exercises at varying levels of difficulty that consolidate the presented concepts and results Includes hints and answers to all exercises via the appendix and is supplemented with an Instructor's Solution Manual
UR  - https://doi.org/10.1007/978-3-031-43713-7
ER  -