1st Edition
by Charalambos A. Charalambides (Author)
A self-contained study of the various applications and developments of discrete distribution theory
Written by a well-known researcher in the field, Discrete q-Distributions features an organized presentation of discrete q-distributions
based on the stochastic model of a sequence of independent Bernoulli
trials. In an effort to keep the book self-contained, the author covers
all of the necessary basic q-sequences and q-functions.
The book begins with an introduction of the notions of a q-power, a q-factorial, and a q-binomial coefficient and proceeds to discuss the basic q-combinatorics and q-hypergeometric series. Next, the book addresses discrete q-distributions with success probability at a trial varying geometrically, with rate q,
either with the number of previous trials or with the number of
previous successes. Further, the book examines two interesting
stochastic models with success probability at any trial varying
geometrically both with the number of trials and the number of successes
and presents local and global limit theorems. Discrete q-Distributions also features:
- Discussions of the definitions and theorems that highlight key concepts and results
- Several worked examples that illustrate the applications of the presented theory
- Numerous
exercises at varying levels of difficulty that consolidate the concepts
and results as well as complement, extend, or generalize the results
- Detailed
hints and answers to all the exercises in an appendix to help
less-experienced readers gain a better understanding of the content
- An
up-to-date bibliography that includes the latest trends and advances in
the field and provides a collective source for further research
- An Instructor’s Solutions Manual available on a companion website
A
unique reference for researchers and practitioners in statistics,
mathematics, physics, engineering, and other applied sciences, Discrete q-Distributions is
also an appropriate textbook for graduate-level courses in discrete
statistical distributions, distribution theory, and combinatorics.