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Negative binomial distribution --- Poisson algebras

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This excellent book will be very useful for students and researchers wishing to learn the basics of Poisson geometry, as well as for those who know something about the subject but wish to update and deepen their knowledge. The authors' philosophy that Poisson geometry is an amalgam of foliation theory, symplectic geometry, and Lie theory enables them to organize the book in a very coherent way.--Alan Weinstein, University of California at BerkeleyThis well-written book is an excellent starting point for students and researchers who want to learn about the basics of Poisson geometry. The topics covered are fundamental to the theory and avoid any drift into specialized questions; they are illustrated through a large collection of instructive and interesting exercises. The book is ideal as a graduate textbook on the subject, but also for self-study.--Eckhard Meinrenken, University of Toronto.

Symplectic geometry --- Poisson brackets --- Poisson manifolds --- Poisson algebras --- Groupoids

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This second edition of Hilbe's Negative Binomial Regression is a substantial enhancement to the popular first edition. The only text devoted entirely to the negative binomial model and its many variations, nearly every model discussed in the literature is addressed. The theoretical and distributional background of each model is discussed, together with examples of their construction, application, interpretation and evaluation. Complete Stata and R codes are provided throughout the text, with additional code (plus SAS), derivations and data provided on the book's website. Written for the practising researcher, the text begins with an examination of risk and rate ratios, and of the estimating algorithms used to model count data. The book then gives an in-depth analysis of Poisson regression and an evaluation of the meaning and nature of overdispersion, followed by a comprehensive analysis of the negative binomial distribution and of its parameterizations into various models for evaluating count data.

Negative binomial distribution --- Poisson algebras --- regressie-analyse --- 519.2 --- 519.2 Probability. Mathematical statistics --- Probability. Mathematical statistics --- Algebras, Poisson --- Associative algebras --- Pascal distribution --- Binomial distribution --- Wiskundige statistiek --- Negative binomial distribution. --- Poisson algebras.

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Poisson structures appear in a large variety of contexts, ranging from string theory, classical/quantum mechanics and differential geometry to abstract algebra, algebraic geometry and representation theory. In each one of these contexts, it turns out that the Poisson structure is not a theoretical artifact, but a key element which, unsolicited, comes along with the problem that is investigated, and its delicate properties are decisive for the solution to the problem in nearly all cases. Poisson Structures is the first book that offers a comprehensive introduction to the theory, as well as an overview of the different aspects of Poisson structures. The first part covers solid foundations, the central part consists of a detailed exposition of the different known types of Poisson structures and of the (usually mathematical) contexts in which they appear, and the final part is devoted to the two main applications of Poisson structures (integrable systems and deformation quantization). The clear structure of the book makes it adequate for readers who come across Poisson structures in their research or for graduate students or advanced researchers who are interested in an introduction to the many facets and applications of Poisson structures.

Geometry, Differential. --- Geometry. --- Hamiltonian systems. --- Poisson algebras. --- Poisson manifolds. --- Symplectic geometry. --- Poisson manifolds --- Poisson algebras --- Engineering & Applied Sciences --- Mathematics --- Physical Sciences & Mathematics --- Geometry --- Applied Mathematics --- Lie algebras. --- Differential geometry --- Algebras, Lie --- Mathematics. --- Nonassociative rings. --- Rings (Algebra). --- Topological groups. --- Lie groups. --- Mathematical analysis. --- Analysis (Mathematics). --- Differential geometry. --- Analysis. --- Differential Geometry. --- Topological Groups, Lie Groups. --- Non-associative Rings and Algebras. --- Algebra, Abstract --- Algebras, Linear --- Lie groups --- Differentiable manifolds --- Global analysis (Mathematics). --- Global differential geometry. --- Topological Groups. --- Algebra. --- Mathematical analysis --- Groups, Topological --- Continuous groups --- Geometry, Differential --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Rings (Algebra) --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups --- 517.1 Mathematical analysis --- Algebraic rings --- Ring theory --- Algebraic fields

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Cluster algebras --- Quantum groups. --- Poisson algebras --- Representations of Lie algebras. --- Lie algebras. --- Algèbres amassées --- Groupes quantiques --- Algèbres de Poisson --- Représentations des algèbres de Lie --- Algèbres de Lie --- Quantum groups --- Representations of Lie algebras --- Lie algebras --- Poisson, Algèbres de --- Représentations d'algèbres de Lie --- Lie, algèbres de --- Algèbres amassées --- Algèbres de Poisson --- Représentations des algèbres de Lie --- Algèbres de Lie --- Groupes quantiques. --- Poisson, Algèbres de. --- Représentations d'algèbres de Lie. --- Lie, Algèbres de.