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Univariate Discrete Distributions, 3rd Edition

ISBN: 978-0-471-71580-1
646 pages
October 2005
Univariate Discrete Distributions, 3rd Edition (0471715808) cover image
This Set Contains:
Continuous Multivariate Distributions, Volume 1, Models and Applications, 2nd Edition by Samuel Kotz, N. Balakrishnan and Normal L. Johnson
Continuous Univariate Distributions, Volume 1, 2nd Edition by Samuel Kotz, N. Balakrishnan and Normal L. Johnson
Continuous Univariate Distributions, Volume 2, 2nd Edition by Samuel Kotz, N. Balakrishnan and Normal L. Johnson
Discrete Multivariate Distributions by Samuel Kotz, N. Balakrishnan and Normal L. Johnson
Univariate Discrete Distributions, 3rd Edition by Samuel Kotz, N. Balakrishnan and Normal L. Johnson

Discover the latest advances in discrete distributions theory

The Third Edition of the critically acclaimed Univariate Discrete Distributions provides a self-contained, systematic treatment of the theory, derivation, and application of probability distributions for count data. Generalized zeta-function and q-series distributions have been added and are covered in detail. New families of distributions, including Lagrangian-type distributions, are integrated into this thoroughly revised and updated text. Additional applications of univariate discrete distributions are explored to demonstrate the flexibility of this powerful method.

A thorough survey of recent statistical literature draws attention to many new distributions and results for the classical distributions. Approximately 450 new references along with several new sections are introduced to reflect the current literature and knowledge of discrete distributions.

Beginning with mathematical, probability, and statistical fundamentals, the authors provide clear coverage of the key topics in the field, including:

  • Families of discrete distributions
  • Binomial distribution
  • Poisson distribution
  • Negative binomial distribution
  • Hypergeometric distributions
  • Logarithmic and Lagrangian distributions
  • Mixture distributions
  • Stopped-sum distributions
  • Matching, occupancy, runs, and q-series distributions
  • Parametric regression models and miscellanea

Emphasis continues to be placed on the increasing relevance of Bayesian inference to discrete distribution, especially with regard to the binomial and Poisson distributions. New derivations of discrete distributions via stochastic processes and random walks are introduced without unnecessarily complex discussions of stochastic processes. Throughout the Third Edition, extensive information has been added to reflect the new role of computer-based applications.

With its thorough coverage and balanced presentation of theory and application, this is an excellent and essential reference for statisticians and mathematicians.

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Preface.

1. Preliminary Information.

2. Families of Discrete Distributions.

3. Binomial Distributions.

4. Poisson Distributions.

5. Neggative Binomial Distributions.

6. Hypergeometric Distributions.

7. Logarithmic and Lagrangian Distributions.

8. Mixture Distributions.

9. Stopped-Sum Distributions.

10. Matching, Occupancy, Runs, and q-Series Distributions.

11. Parametric Regression Models and Miscellanea.

Bibliography.

Abbreviations.

Index.

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NORMAN L. JOHNSON, PHD, was Professor Emeritus, Department of Statistics, University of North Carolina at Chapel Hill. Dr. Johnson was Editor-in-Chief (with Dr. Kotz) of the Encyclopedia of Statistical Sciences, Second Edition (Wiley).

ADRIENNE W. KEMP, PHD, is Honorary Senior Lecturer at the Mathematical Institute, University of St. Andrews in Scotland.

SAMUEL KOTZ, PHD, is Professor and Research Scholar, Department of Engineering Management and Systems Engineering, The George Washington University in Washington, DC.

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“With its thorough coverage and balanced presentation of theory and application, this is an excellent and essential reference for statisticians and mathematicians.”  (Xolosepo, 27 October 2012)

"The authors continue to do a praise-worthy job of making the material accessible in the third edition. This book should be on every library's shelf." (Journal of the American Statistical Association, September 2006)

"These authors have achieved considerable renown for their comprehensive books on statistical distributions." (Technometrics, August 2006)

"Encyclopedic in nature, the book continues to be a valuable reference." (Mathematical Reviews, 2006d)

"This is an important book that should be part of every statistician's library." (MAA Reviews, January 2, 2006)

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