03631nam a22005655i 4500 978-3-031-43713-7 DE-He213 20251030110837.0 cr nn 008mamaa 231122s2024 sz | s |||| 0|eng d 9783031437137 978-3-031-43713-7 10.1007/978-3-031-43713-7 doi QA297.4 PBD bicssc MAT008000 bisacsh PBD thema Charalambides, Charalambos A. author. aut http://id.loc.gov/vocabulary/relators/aut 67425 Multivariate Discrete q-Distributions [electronic resource] / by Charalambos A. Charalambides. 1st ed. 2024. Cham : Springer Nature Switzerland : Imprint: Springer, 2024. XI, 127 p. 2 illus. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Synthesis Lectures on Mathematics & Statistics, 1938-1751 Preface -- Multivariate q-Combinatorics and q-Hypergeometric Series -- Multivariate q-Distributions -- Appendix: Hints and Answers to Exercises -- Bibliography -- Index. 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. Discrete mathematics. Probabilities. 65724 Mathematics. 65523 Distribution (Probability theory). 67426 Discrete Mathematics. Applications of Discrete Mathematics. 67427 Probability Theory. 67428 Applied Probability. 65727 Applications of Mathematics. 65529 Distribution Theory. 67429 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031437120 Printed edition: 9783031437144 Printed edition: 9783031437151 Synthesis Lectures on Mathematics & Statistics, 1938-1751 https://doi.org/10.1007/978-3-031-43713-7 ZDB-2-SXSC 56601 56601