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Generalized Poisson distributions. Properties and applications. (English) Zbl 0691.62015

Statistics: Textbooks and Monographs, 99. New York etc.: Marcel Dekker, Inc. X, 302 p. $ 107.50 (1989).
The book is devoted to the generalized Poisson distribution (GPD) with the probability function \[ P_ x(\theta,\lambda)=(\theta (\theta +x\lambda)^{x-1}e^{-\theta -x-\lambda})/x!,\quad x=0,1,2,...\quad. \] The text is divided into 10 chapters: 1. Generalized Poisson distribution and some of its descriptive properties; 2. Models leading to the GPD; 3. Other important properties of the GPD; 4. Statistical estimation; 5. Applications; 6. Confidence interval estimation; 7. Statistical testing; 8. Some characterizations; 9. Truncated GPD models, error analysis for negative \(\lambda\), and some unsolved problems; 10. Computer programs.
The monograph offers a systematic treatment of the GPD. Every published theorem and formula is stated in full with a complete reference. Some new results have also been given. The proofs are included for some theorems so that the description is logical and interesting. Some applications of the model are discussed. The book should be of interest to research workers in applied statistics, to engineers involved in discrete pattern recognition and to investigators in various fields of application. The material can be also used as a special course for upper-level undergraduate students or graduate students.
Reviewer: J.Bartoszewicz

MSC:

62E10 Characterization and structure theory of statistical distributions
62-02 Research exposition (monographs, survey articles) pertaining to statistics
62E15 Exact distribution theory in statistics
62F03 Parametric hypothesis testing
62F10 Point estimation
60-02 Research exposition (monographs, survey articles) pertaining to probability theory
60E05 Probability distributions: general theory
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