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Probabilities --- Random variables --- Characteristic functions --- Probabilités --- Variables aléatoires --- Fonctions caractéristiques

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Interest in the skew-normal and related families of distributions has grown enormously over recent years, as theory has advanced, challenges of data have grown, and computational tools have made substantial progress. This comprehensive treatment, blending theory and practice, will be the standard resource for statisticians and applied researchers. Assuming only basic knowledge of (non-measure-theoretic) probability and statistical inference, the book is accessible to the wide range of researchers who use statistical modelling techniques. Guiding readers through the main concepts and results, it covers both the probability and the statistics sides of the subject, in the univariate and multivariate settings. The theoretical development is complemented by numerous illustrations and applications to a range of fields including quantitative finance, medical statistics, environmental risk studies, and industrial and business efficiency. The author's freely available R package sn, available from CRAN, equips readers to put the methods into action with their own data.

Distribution (Probability theory) --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Mathematical Sciences --- Probability

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Random variables --- Variables aléatoires. --- Characteristic functions --- Fonctions caractéristiques. --- Distribution (théorie des probabilités) --- Distribution (Probability theory)

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This book demonstrates current trends in research on combinatorial and computational commutative algebra with a primary emphasis on topics related to monomial ideals. Providing a useful and quick introduction to areas of research spanning these fields, Monomial Ideals is split into three parts. Part I offers a quick introduction to the modern theory of Gröbner bases as well as the detailed study of generic initial ideals. Part II supplies Hilbert functions and resolutions and some of the combinatorics related to monomial ideals including the Kruskal—Katona theorem and algebraic aspects of Alexander duality. Part III discusses combinatorial applications of monomial ideals, providing a valuable overview of some of the central trends in algebraic combinatorics. Main subjects include edge ideals of finite graphs, powers of ideals, algebraic shifting theory and an introduction to discrete polymatroids. Theory is complemented by a number of examples and exercises throughout, bringing the reader to a deeper understanding of concepts explored within the text. Self-contained and concise, this book will appeal to a wide range of readers, including PhD students on advanced courses, experienced researchers, and combinatorialists and non-specialists with a basic knowledge of commutative algebra. Since their first meeting in 1985, Juergen Herzog (Universität Duisburg-Essen, Germany) and Takayuki Hibi (Osaka University, Japan), have worked together on a number of research projects, of which recent results are presented in this monograph.

Algebra. --- Mathematics. --- Commutative algebra --- Combinatorial analysis --- Grèobner bases --- Characteristic functions --- Mathematics --- Physical Sciences & Mathematics --- Algebra --- Commutative algebra. --- Commutative rings. --- Commutative Rings and Algebras. --- Mathematical analysis --- Characteristic functions. --- Combinatorial analysis. --- Gröbner bases. --- Rings (Algebra)

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The notions of transfer function and characteristic functions proved to be fundamental in the last fifty years in operator theory and in system theory. Moshe Livsic played a central role in developing these notions, and the book contains a selection of carefully chosen refereed papers dedicated to his memory. Topics include classical operator theory, ergodic theory and stochastic processes, geometry of smooth mappings, mathematical physics, Schur analysis and system theory. The variety of topics attests well to the breadth of Moshe Livsic's mathematical vision and the deep impact of his work.

Characteristic functions. --- Light -- Scattering. --- Scattering (Physics). --- Transfer functions. --- Mathematics --- Calculus --- Mathematical Statistics --- Physical Sciences & Mathematics --- Characteristic functions --- Scattering (Mathematics) --- Transfer functions --- Operator theory --- Ergodic theory --- Functions, Transfer --- Scattering theory (Mathematics) --- Characteristic formula of an ideal --- Characteristic Hilbert functions --- Functions, Characteristic --- Functions, Hilbert --- Hilbert characteristic functions --- Hilbert functions --- Hilbert's characteristic functions --- Hilbert's functions --- Postulation formula --- Mathematics. --- Operator theory. --- Operator Theory. --- Probabilities --- Automatic control --- Control theory --- Boundary value problems --- Differential equations, Partial --- Scattering operator --- Functional analysis