Multivariate Discrete q-Distributions

Charalambos A. Charalambides

Nov 2023 · Springer Nature

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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

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Charalambos A. Charalambides, PhD, is Professor Emeritus of mathematical statistics at the University of Athens, Greece, where he has been lecturer, assistant, associate and (full) professor from 1972 to 2010. Dr. Charalambides received a diploma in mathematics (1969) and a PhD in mathematical statistics (1972) from the University of Athens. He was visiting assistant professor at McGill University, Montreal, Canada (1973-74), visiting associate professor at Temple University, Philadelphia, USA (1985-86), and visiting professor at the University of Cyprus, Nicosia, Cyprus (1995-96, 2003-04, 2007-08, 2010-11). Since 1979 he has been elected member of the International Statistical Institute (ISI). His research interests include enumerative combinatorics, combinatorial probability and parametric inference/point estimation.

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