This book presents a comprehensive study of symmetric multivariate and related distributions, focusing on their construction, properties, and applications. The authors, Kai-Tai Fang, Samuel Kotz, and Kai-Wang Ng, provide a detailed exploration of various types of symmetric distributions, including spherical, elliptically symmetric, and $\alpha$-symmetric distributions. The book also discusses the Dirichlet distribution, which is a fundamental multivariate distribution with wide applications in statistics and probability theory. The authors begin by introducing the concept of symmetric multivariate distributions and their construction through various methods, such as density functions, characteristic functions, and stochastic decomposition. They then delve into the properties of these distributions, including their marginal and conditional distributions, moments, and relationships with other distributions. The book also covers the concept of invariance under group transformations and its implications for symmetric distributions. A significant portion of the book is dedicated to the Dirichlet distribution, which is a basic multivariate distribution used in many statistical models. The authors provide a detailed discussion of its properties, including its moments, variances, and covariances. They also explore its applications in statistical modeling, distribution theory, and Bayesian inference. The book is structured into chapters that cover various aspects of symmetric multivariate distributions, including their definitions, properties, and applications. Each chapter includes problems and exercises to help readers understand and apply the concepts discussed. The authors also provide references to further reading and an extensive index for easy reference. Overall, this book is a valuable resource for statisticians and researchers interested in symmetric multivariate distributions. It provides a thorough treatment of the subject, covering both theoretical and practical aspects. The book is well-organized, with clear explanations and detailed proofs, making it accessible to readers with a background in statistics and probability theory. The authors' expertise in the field is evident throughout the book, and their contributions to the study of symmetric multivariate distributions are highlighted in the text. The book is an essential reference for anyone working in the field of multivariate statistics and related areas.This book presents a comprehensive study of symmetric multivariate and related distributions, focusing on their construction, properties, and applications. The authors, Kai-Tai Fang, Samuel Kotz, and Kai-Wang Ng, provide a detailed exploration of various types of symmetric distributions, including spherical, elliptically symmetric, and $\alpha$-symmetric distributions. The book also discusses the Dirichlet distribution, which is a fundamental multivariate distribution with wide applications in statistics and probability theory. The authors begin by introducing the concept of symmetric multivariate distributions and their construction through various methods, such as density functions, characteristic functions, and stochastic decomposition. They then delve into the properties of these distributions, including their marginal and conditional distributions, moments, and relationships with other distributions. The book also covers the concept of invariance under group transformations and its implications for symmetric distributions. A significant portion of the book is dedicated to the Dirichlet distribution, which is a basic multivariate distribution used in many statistical models. The authors provide a detailed discussion of its properties, including its moments, variances, and covariances. They also explore its applications in statistical modeling, distribution theory, and Bayesian inference. The book is structured into chapters that cover various aspects of symmetric multivariate distributions, including their definitions, properties, and applications. Each chapter includes problems and exercises to help readers understand and apply the concepts discussed. The authors also provide references to further reading and an extensive index for easy reference. Overall, this book is a valuable resource for statisticians and researchers interested in symmetric multivariate distributions. It provides a thorough treatment of the subject, covering both theoretical and practical aspects. The book is well-organized, with clear explanations and detailed proofs, making it accessible to readers with a background in statistics and probability theory. The authors' expertise in the field is evident throughout the book, and their contributions to the study of symmetric multivariate distributions are highlighted in the text. The book is an essential reference for anyone working in the field of multivariate statistics and related areas.