Johnson N.L., Kemp A.W., Kotz S. Univariate Discrete Distributions

John Wiley, 2005. — 675 p.This book is dedicated to the memory of Professor N. L. Johnson, who passed away during the production stages. He was my longtime friend and mentor; his assistance with this revision during his long illness is greatly appreciated. His passing is a sad loss to all who are interested in statistical distribution theory.
The preparation of the third edition gave Norman and I the opportunity to substantially revise and reorganize parts of the book. This enabled us to increase the coverage of certain areas and to highlight today’s better understanding of interrelationships between distributions. Also a number of errors and inaccuracies in the two previous editions have been corrected and some explanations are clarified.
The continuing interest in discrete distributions is evinced by the addition of over 400 new references, nearly all since 1992. Electronic databases, such as Statistical Theory and Methods Abstracts (published by the International Statistical Institute), the Current Index to Statistics: Applications, Methods and Theory (published by the American Statistical Association and the Institute of Mathematical Statistics), and the Thomson ISI Web of Science, have drawn to our attention papers and articles which might otherwise have escaped notice.
It is important to acknowledge the impact of scholarly, encyclopedic publications such as the Dictionary and Bibliography of Statistical Distributions in Scientific Work, Vol. 1: Discrete Models, by G. P. Patil, M. T. Boswell, S. W. Joshi, and M. V. Ratnaparkhi (1984) (published by the International Co-operative Publishing House, Fairland, MD), and the Thesaurus of Univariate Discrete Probability Distributions, by G. Wimmer and G. Altmann (1999) (published by Stamm Verlag, Essen). The new edition of Statistical Distributions, by M. Evans, N. Peacock, and B. Hastings (2000) (published by Wiley, New York), encouraged us to address the needs of occasional readers as distinct from researchers into the theoretical and applied aspects of the subject.
The objectives of this book are far wider. It aims, as before, to give an account of the properties and the uses of discrete distributions at the time of writing, while adhering to the same level and style as previous editions. The 1969 intention to exclude theoretical minutiae of no apparent practical importance has not been forgotten. We have tried to give a balanced account of new developments, especially those in the more accessible statistical journals. There has also been relevant work in related fields, such as econometrics, combinatorics, probability theory, stochastic processes, actuarial studies, operational research, and social sciences. We have aimed to provide a framework within which future research findings can best be understood.
In trying to keep the book to a reasonable length, some material that should have been included was omitted or its coverage curtailed. Comments and criticisms are welcome; I would like to express our gratitude to friends and colleagues for pointing out faults in the last edition and for their input of ideas into the new edition.Preliminary Information
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