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**Univariate discrete distributions.
2. ed.**
*(English)*
Zbl 0773.62007

Wiley Series in Probability and Mathematical Statistics. Probability and Mathematical Statistics. New York: John Wiley & Sons. xx, 565 p. (1992).

More than two decades elapsed since the first edition of this book on discrete distributions (see the review Zbl 0292.62009) as the first volume of a well-known tetralogy on distributions in statistics. Now, Adrienne W. Kemp joined the first two authors for the second edition of this classical reference work.

Entirely devoted to the univariate case, the text has been brought up-to- date with a considerable number of improvements and additions, preserving however the structure of the first edition. Major and substantial changes are in Chapters 1-7 (preliminary information; families of discrete distributions; binomial, Poisson, negative binomial distributions; hypergeometric, logarithmic distributions). Chapters 8 and 9 now concern mixtures of distributions and stopped-sum distributions, respectively. Chapter 10 deals with matching, occupancy, and runs distributions, expanded with material on distributions of order \(k\). The new Chapter 11 on various other discrete distributions, not easily fitting in the previous chapters, replaces the former Chapter 11 devoted to the multivariate case. The results are presented in organized fashion and as fluid as possible.

An extensive bibliography of 75 pages including most of the results through 1991 accompanies the text. The authors succeded admirably in bringing the reader up-to-date with the present situation in discrete distributions by getting in such an amount of information within a reasonable size of the volume. The new edition retains the encyclopedic character of the first one and should appeal to a wide variety of researchers and students, launching them on many current research problems.

Entirely devoted to the univariate case, the text has been brought up-to- date with a considerable number of improvements and additions, preserving however the structure of the first edition. Major and substantial changes are in Chapters 1-7 (preliminary information; families of discrete distributions; binomial, Poisson, negative binomial distributions; hypergeometric, logarithmic distributions). Chapters 8 and 9 now concern mixtures of distributions and stopped-sum distributions, respectively. Chapter 10 deals with matching, occupancy, and runs distributions, expanded with material on distributions of order \(k\). The new Chapter 11 on various other discrete distributions, not easily fitting in the previous chapters, replaces the former Chapter 11 devoted to the multivariate case. The results are presented in organized fashion and as fluid as possible.

An extensive bibliography of 75 pages including most of the results through 1991 accompanies the text. The authors succeded admirably in bringing the reader up-to-date with the present situation in discrete distributions by getting in such an amount of information within a reasonable size of the volume. The new edition retains the encyclopedic character of the first one and should appeal to a wide variety of researchers and students, launching them on many current research problems.

Reviewer: R.Theodorescu (Quebec)

### MSC:

62Exx | Statistical distribution theory |

62-02 | Research exposition (monographs, survey articles) pertaining to statistics |

60Exx | Distribution theory |

60-02 | Research exposition (monographs, survey articles) pertaining to probability theory |

62-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistics |

60-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to probability theory |