Discrete multivariate distributions. (English) Zbl 0868.62048

Johnson, Norman L.; Kotz, Samuel; Balakrishnan, N.

Wiley Series in Probability and Statistics. New York, NY: Wiley. xxii, 299 p. (1997).

This book grew out of the 11th chapter of the first edition of “Distributions in statistics: Discrete distributions”. (1969; Zbl 0292.62009). It is the fourth volume of the second edition. After an introductory chapter, giving an overview the tools and concepts to be used later on, each of the following chapters deals with a specific family of multivariate distributions (md): Multinomial d., Negative multinomial and other multinomial-related d., M. Poisson d., M. power series d., M. hypergeometric and related d., M. Pólya-Eggenberger d., M. Ewens d., M. d. of order \(s\), and Miscellaneous d. Most of these distributions are closely related to the univariate discrete distributions described by N. L. Johnson, S. Kotz, and A. W. Kemp [Univariate discrete distributions. 2. ed. (1992; Zbl 0773.62007)].
For each distribution, properties, moments, estimation methods, and some applications are presented. Random number generation is discussed for some of them. In addition, in each chapter a number of issues specific to its respective distribution are discussed. At the end of each chapter a bibliography is given. As with the other volumes of “Distributions in statistics”, this one will be the main source over the next decades for all interested in using them or doing research in this field.

Reviewer: R.Schlittgen (Hamburg)

MSC:

62H10	Multivariate distribution of statistics
62-02	Research exposition (monographs, survey articles) pertaining to statistics
62-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistics
62H05	Characterization and structure theory for multivariate probability distributions; copulas
62H12	Estimation in multivariate analysis

Keywords:

Polya-Eggenberger; random number generation; multinomial; negative multinomial; Poisson; power series; hypergeometric; Ewens; moments; estimation methods

Citations:

Zbl 0292.62009; Zbl 0773.62007