Symmetric Multivariate and Related Distributions

Symmetric Multivariate and Related Distributions

1990 | Kai Wang Fang, Samuel Kotz, Kai Wang Ng
The book "Symmetric Multivariate and Related Distributions" by K.-T. Fang, S. Kotz, and K.W. Ng, published in 1989 and reprinted in 2018, is a comprehensive monograph on multivariate symmetric distributions. The authors aim to compile and digest widely scattered information on multivariate symmetric distributions that have appeared in the literature over the past two decades. The book covers various aspects of symmetric multivariate distributions, including their construction, properties, and applications. The first chapter provides a unified approach to constructing symmetric multivariate distributions, laying the mathematical foundation for the subsequent chapters. It discusses different methods of extending univariate distributions to multivariate analogues, such as density, characteristic function, linear combinations, and stochastic decomposition. The chapter also explores the concept of symmetry in multivariate distributions, including spherical distributions, elliptical distributions, and $\ell_1$-norm symmetric distributions. Subsequent chapters delve into specific types of symmetric multivariate distributions, such as spherical distributions, elliptical distributions, and $\alpha$-symmetric distributions. The book also covers characterizations of symmetric distributions, robust statistics, regression models, and the analysis of contingency tables. The authors provide detailed proofs and examples to illustrate the concepts and results presented. The book is intended for researchers and practitioners in statistics, probability theory, and related fields who are interested in the theory and applications of symmetric multivariate distributions. It serves as a valuable resource for understanding the properties and applications of these distributions in various statistical models and methodologies.The book "Symmetric Multivariate and Related Distributions" by K.-T. Fang, S. Kotz, and K.W. Ng, published in 1989 and reprinted in 2018, is a comprehensive monograph on multivariate symmetric distributions. The authors aim to compile and digest widely scattered information on multivariate symmetric distributions that have appeared in the literature over the past two decades. The book covers various aspects of symmetric multivariate distributions, including their construction, properties, and applications. The first chapter provides a unified approach to constructing symmetric multivariate distributions, laying the mathematical foundation for the subsequent chapters. It discusses different methods of extending univariate distributions to multivariate analogues, such as density, characteristic function, linear combinations, and stochastic decomposition. The chapter also explores the concept of symmetry in multivariate distributions, including spherical distributions, elliptical distributions, and $\ell_1$-norm symmetric distributions. Subsequent chapters delve into specific types of symmetric multivariate distributions, such as spherical distributions, elliptical distributions, and $\alpha$-symmetric distributions. The book also covers characterizations of symmetric distributions, robust statistics, regression models, and the analysis of contingency tables. The authors provide detailed proofs and examples to illustrate the concepts and results presented. The book is intended for researchers and practitioners in statistics, probability theory, and related fields who are interested in the theory and applications of symmetric multivariate distributions. It serves as a valuable resource for understanding the properties and applications of these distributions in various statistical models and methodologies.
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